1. 16 + 4 x (7 + 8) - 3 = ________?
= 16 + 4 x (15) - 3
= 16 + 60 - 3
= 16 + 57
= 73 *Ans.
2. (18 + 17) (12 + 9)
- (7 x 16) (4 + 2) = ________?
= (35) (21) - (112) (6)
= 735 - 672
= 63 *Ans.
= (35) (21) - (112) (6)
= 735 - 672
= 63 *Ans.
3. The sum of 73, 2891, 406 and
98 is _______?
= 73 + 2891 + 406 + 98
= 3468 *Ans.
= 73 + 2891 + 406 + 98
= 3468 *Ans.
4. Which of the following numbers
is divisible by 24 ?
192 ÷ 24 = 8 *Ans.
286 ÷ 24 = 11 remainder 4, 268 not divisible by 24 because it has a remainder when divided by 24.
192 ÷ 24 = 8 *Ans.
286 ÷ 24 = 11 remainder 4, 268 not divisible by 24 because it has a remainder when divided by 24.
5. Which of the following numbers is prime?
a. 57 = 3 x 19
b. 87 = 3 x 29
c. 89 = 89 x 1 *Ans.
d. 91 = 13 x 7
a. 57 = 3 x 19
b. 87 = 3 x 29
c. 89 = 89 x 1 *Ans.
d. 91 = 13 x 7
Mathematics
Test I Solution - Page 60
6. The product of 18 and 73 is ______?
18 x 73 = 1,314
1314 *Ans.
6. The product of 18 and 73 is ______?
18 x 73 = 1,314
1314 *Ans.
7. The difference of 476 and 182 is
_______?
476 - 182 = 294
294 *Ans.
476 - 182 = 294
294 *Ans.
8. Evaluate 1
+ 2 + 3 =
______?
100 1000 10
1 / 100 = 0.01
2 / 1000 = 0.02
3 / 10 = 0.3
0.01 + 0.02 + 0.3 = 0.312 *Ans
100 1000 10
1 / 100 = 0.01
2 / 1000 = 0.02
3 / 10 = 0.3
0.01 + 0.02 + 0.3 = 0.312 *Ans
9. Evaluate ½ + ¼ + ⅛
_________.
Find first the LCD which is 8.
½ = 4/8
¼ = 2/8
⅛ = 1/8
= 4 + 2 + 1
8 8 8
= 7/8 *Ans.
Find first the LCD which is 8.
½ = 4/8
¼ = 2/8
⅛ = 1/8
= 4 + 2 + 1
8 8 8
= 7/8 *Ans.
10. Seventy-one and twenty-one ten thousandths is written in
standard form as :
71.0021 *Ans.
71.0021 *Ans.
Mathematics
Test I Solution - Page 61
11. One thousand forty two and seven thousandths written form is _____?
= 1, 042.007 *Ans.
11. One thousand forty two and seven thousandths written form is _____?
= 1, 042.007 *Ans.
12. 1 + 5 + 1
= _______?
3 6 2
Find first the LCD which is = 6
3 6 2
Find first the LCD which is = 6
1/3 is now 2/6
5/6 is still 5/6
1/2 is now 3/6
= 2 + 5 + 3
6
= 10/6 or 5/3
1 ⅔ *Ans.
13. 3 ½ - 1 ⅔ = ________?
Change 3 ½ to improper fraction which is 7/2
Change 1 ⅔ to improper fraction which is 5/3
= 7 - 5
2 3
= 3(7) - 2(5)
2(3)
= 21 - 10
6
= 11/6
= 1 5 *Ans.
6
Change 3 ½ to improper fraction which is 7/2
Change 1 ⅔ to improper fraction which is 5/3
= 7 - 5
2 3
= 3(7) - 2(5)
2(3)
= 21 - 10
6
= 11/6
= 1 5 *Ans.
6
14. 900 x 0.09 = _________?
900
x .09
81.00 *Ans.
900
x .09
81.00 *Ans.
Mathematics
Test I Solution - Page 62
15. 7 ÷ 21 = ___________?
8 4
= 7 x 4
8 21
= 28
168
= 28 ÷ 28
168 ÷ 28
= 1/6 *Ans.
15. 7 ÷ 21 = ___________?
8 4
= 7 x 4
8 21
= 28
168
= 28 ÷ 28
168 ÷ 28
= 1/6 *Ans.
16. 3 x 10 = ______?
5 3
= 30 / 15
= 2 *Ans.
5 3
= 30 / 15
= 2 *Ans.
17. 3.156 x 0.12 = ________?
3.156 ------> 3-decimal places
x .12 ------> 2-decimal places
6312
3156
0.37872 *Ans. ------> 5-decimal places
3.156 ------> 3-decimal places
x .12 ------> 2-decimal places
6312
3156
0.37872 *Ans. ------> 5-decimal places
18. 5 ½ ÷ 2 ⅓ = ______?
= 11 ÷ 7
2 3
= 11 x 3
2 7
= 33
14
change 33/14 to improper fraction by dividing 33 by 14 which is :
2 5 *Ans.
14
= 11 ÷ 7
2 3
= 11 x 3
2 7
= 33
14
change 33/14 to improper fraction by dividing 33 by 14 which is :
2 5 *Ans.
14
Mathematics
Test I Solution - Page 63
19. 2 + 4 = _________.
1 1
2 3
6
= 3 2
6 6
6
= 5
6
= 6 x 6
5
= 36/5
= 7 ⅕ Ans.
19. 2 + 4 = _________.
1 1
2 3
6
= 3 2
6 6
6
= 5
6
= 6 x 6
5
= 36/5
= 7 ⅕ Ans.
20. 3% of 24 = _____?
= 0.03 x 24
= 0.72 *Ans.
= 0.03 x 24
= 0.72 *Ans.
21. 1402 + 142 + 14.2 + 1.42 = _________?
1402.00
142.00
+ 14.20
1.42
1559.62 *Ans.
1402.00
142.00
+ 14.20
1.42
1559.62 *Ans.
22. 2010 x 0.00001 = _________?
2010 x .00001 = 0.2010
=0.210 *Ans.
2010 x .00001 = 0.2010
=0.210 *Ans.
23. Find the average of 6.8, 3.5,
9.2, 7.45, and 6.05.
= 6.8 + 3.5 + 9.2 + 7.45 + 6.05
5
= 33/5
= 6.6 *Ans.
= 6.8 + 3.5 + 9.2 + 7.45 + 6.05
5
= 33/5
= 6.6 *Ans.
25. 87 / 0.01 = __________?
move the decimal point 2 places to the right in both dividend & divisor because there are 2 decimal places in the divisor.
0.01 is now 1 and 87 is now 8700
= 8700 / 1
= 8700 *Ans.
move the decimal point 2 places to the right in both dividend & divisor because there are 2 decimal places in the divisor.
0.01 is now 1 and 87 is now 8700
= 8700 / 1
= 8700 *Ans.
26. (0.5) (5) (0.5) = ________.
= (2.5) (0.5)
= 1.25 *Ans.
= (2.5) (0.5)
= 1.25 *Ans.
27. Dividing by 0.2 is the same as multiplying by ________?
= 1 ÷ 0.2
= 1 ÷ 2
10
= 1 ÷ 1
5
= 1 x 5
= 5 *Ans.
= 1 ÷ 0.2
= 1 ÷ 2
10
= 1 ÷ 1
5
= 1 x 5
= 5 *Ans.
28. 0.012 ÷ 3 = ________?
.004
= 3 | .012
0
1
0
12
12
0
0.004 *Ans.
.004
= 3 | .012
0
1
0
12
12
0
0.004 *Ans.
29. 2.944 ÷ 0.23 = _______?
move the decimal point 2 places to the right in both dividend & divisor because there are 2 decimal places in the divisor.
0.23 is now 23 and 2.944 is now 294.4
= 294.4 / 23
= 12.8 *Ans.
move the decimal point 2 places to the right in both dividend & divisor because there are 2 decimal places in the divisor.
0.23 is now 23 and 2.944 is now 294.4
= 294.4 / 23
= 12.8 *Ans.
Mathematics
Test I Solution - Page 65
30. 0.25 + 0.25 + 0.25 + 0.25 = _________?
0.25
= 4 (0.25)
0.25
= 4 *Ans.
30. 0.25 + 0.25 + 0.25 + 0.25 = _________?
0.25
= 4 (
= 4 *Ans.
31. 0.0088 ÷ 0.22 =
________?
To start dividing, you have to make the divisor 0.22 a whole number by moving the decimal point 2 places to the right. Doing this will also move two decimal point for the dividend 00.0088.
0.22 is now 22 and 0.0088 is now 0.88
0.04
22 | 0.88
0
88
88
0
therefore, 0.04 *Ans.
To start dividing, you have to make the divisor 0.22 a whole number by moving the decimal point 2 places to the right. Doing this will also move two decimal point for the dividend 00.0088.
0.22 is now 22 and 0.0088 is now 0.88
0.04
22 | 0.88
0
88
88
0
therefore, 0.04 *Ans.
32. (0.15 x 0.37) + (0.85 + 0.63) +
(0.15 + 0.63) + (0.85 + 0.37) = _______?
= [(0.15 + 0.63) + (0.85 + 0.63)] + [(0.15 x 0.37) + (0.85 + 0.37)]
= [0.63 (0.15 + 0.85)] + [0.37(0.15 + 0.85)]
= [0.63 (1)] + [0.37(1)]
= 1 *Ans.
= [(0.15 + 0.63) + (0.85 + 0.63)] + [(0.15 x 0.37) + (0.85 + 0.37)]
= [0.63 (0.15 + 0.85)] + [0.37(0.15 + 0.85)]
= [0.63 (1)] + [0.37(1)]
= 1 *Ans.
33. Which of the following best approximate
68 / 0.17 = ____?
To start dividing, you have to make the divisor 0.17 a whole number by moving the decimal point 2 places to the right. Doing this will also move two decimal point for the dividend 68.
0.17 is now 17 and 68 is now 6800
=6800 / 17
= 400 *Ans.
To start dividing, you have to make the divisor 0.17 a whole number by moving the decimal point 2 places to the right. Doing this will also move two decimal point for the dividend 68.
0.17 is now 17 and 68 is now 6800
=6800 / 17
= 400 *Ans.
34. The decimal from of 11/6 is ______?
= 11
6
= 1.83 *Ans.
= 11
6
= 1.83 *Ans.
35. 5/9 of what number is 435 ?
5 x N = 435
9
N = 435 ( 9 )
5
N = 783 *Ans.
5 x N = 435
9
N = 435 ( 9 )
5
N = 783 *Ans.
Mathematics
Test I Solution - Page 66
36. Which of the following fractions is the greatest?
a. 1 / 10 = 1 / 10
b. 0.1 = 1 = 1
0.10 1.0
c. 1 = 100 ---> 100
0.01 1
d. 1 = 1000 -----> 1000 *Ans
0.001 1
36. Which of the following fractions is the greatest?
a. 1 / 10 = 1 / 10
b. 0.1 = 1 = 1
0.10 1.0
c. 1 = 100 ---> 100
0.01 1
d. 1 = 1000 -----> 1000 *Ans
0.001 1
37. 4.7 - 3.12 = _______?
4.70 - 3.12 = 1.58 *Ans.
4.70 - 3.12 = 1.58 *Ans.
38. 19.4 - 12.72 + 5 ______?
19.4 + 5 = 24.40 - 12.72 = 11.68 *Ans.
19.4 + 5 = 24.40 - 12.72 = 11.68 *Ans.
39. 27 ÷ -3 = _______?
32 8
= 27 x ( 8 )
32 -3
= 216 ÷ 24
-96 ÷ 24
= 9
-4
= -2 ¼ *Ans.
32 8
= 27 x ( 8 )
32 -3
= 216 ÷ 24
-96 ÷ 24
= 9
-4
= -2 ¼ *Ans.
40. 2 ¾ x 4 = ________?
= 11 x4
4
= 11 *Ans.
= 11 x
= 11 *Ans.
42. (-11.1) + (12.32) = _________.
12.32
- 11.1
1.22 *Ans.
12.32
- 11.1
1.22 *Ans.
43. What % of 50 is 15?
B = 50; P = 15
Rate = P x 100%
B
= 15 x 100%
50
= 3 x 100%
100
= 30% *Ans.
B = 50; P = 15
Rate = P x 100%
B
= 15 x 100%
50
= 3 x 100%
100
= 30% *Ans.
44. What % of 12 is 6 ?
Rate = P x 100%
B
= 6 x 100%
12
= 1 x 100%
2
= 50% *Ans.
Rate = P x 100%
B
= 6 x 100%
12
= 1 x 100%
2
= 50% *Ans.
45. 36 / 720 = __________?
.05
720 | 36.00
36.00
0
therefore 0.05 *Ans.
.05
720 | 36.00
36.00
0
therefore 0.05 *Ans.
Mathematics
Test I Solution - Page 68
46. What is 1/4 % of 880?
= 1/4 % x 880
= 1/400 x 880
= 880/400
= 2.2 *Ans.
46. What is 1/4 % of 880?
= 1/4 % x 880
= 1/400 x 880
= 880/400
= 2.2 *Ans.
47. What % of 2 and 1/2 is 1/2 ?
Rate = 1/2 x 100%
2 ½
= ½ x 100%
5/2
= 1 x 2 x 100%
2 5
= 1 x 100%
5
= 20% *Ans.
Rate = 1/2 x 100%
2 ½
= ½ x 100%
5/2
= 1 x 2 x 100%
2 5
= 1 x 100%
5
= 20% *Ans.
48. 180 is 66 ⅔ % of what number?
⅔ N = 180
N = 180 ( 3 )
2
N = 270 *Ans.
⅔ N = 180
N = 180 ( 3 )
2
N = 270 *Ans.
49. ⅓ of what number is
42 ?
⅓ x N = 42
N = 42 ÷ ⅓
N = 42 x 3
N = 126 *Ans.
⅓ x N = 42
N = 42 ÷ ⅓
N = 42 x 3
N = 126 *Ans.
50. 8 ⅓ - 2 5 =
________?
8
8 ⅓ = 25/3
2 5 = 21/8
8
= 25 - 21
3 8
= 8(25) - 3(21)
3(8)
= 200 - 63
24
= 137
24
= 5 17 *Ans.
24
8
8 ⅓ = 25/3
2 5 = 21/8
8
= 25 - 21
3 8
= 8(25) - 3(21)
3(8)
= 200 - 63
24
= 137
24
= 5 17 *Ans.
24
Mathematics
Test II Solution - Page 69
Solutions
1. 27, 499 round to the nearest hundred is _______?
= 27, 499 ---> drop 99 and change it to 00 and add 1 to the next digit which is 4 since 99 is more than 50.
Therefore 27,500 is the answer. *Ans.
Solutions
1. 27, 499 round to the nearest hundred is _______?
= 27, 499 ---> drop 99 and change it to 00 and add 1 to the next digit which is 4 since 99 is more than 50.
Therefore 27,500 is the answer. *Ans.
2. Twenty-four weeks is how many days?
= 24weeks x 7 days
weeks
= 24 x 7 days
= 168 days *Ans.
= 24
= 24 x 7 days
= 168 days *Ans.
3. Five hundred ninety-five days is how many weeks?
= 595days x 1 week
7days
= 595 week
7
= 85 weeks *Ans.
= 595
7
= 595 week
7
= 85 weeks *Ans.
4. Eighteen bus loads of 56 students each went to join the Independence Day Celebration. One hundred seventy-four did not go. How many students are there in all?
Number of students :
N = (18 x 56) + 174
= 1008 (174)
= 1182 students *Ans.
5. Richard bowled 3 games and got scores of 139, 153, and
128. What was his average score for the three games?
Average = 139 + 153 + 128
3
= 420
3
= 140 *Ans.
Average = 139 + 153 + 128
3
= 420
3
= 140 *Ans.
Mathematics
Test II Solution - Page 70
6. What time will it be 3 and 1/2 hours after 7:15 PM?
= 7:15 + 3:30
= 10: 45 PM *Ans.
6. What time will it be 3 and 1/2 hours after 7:15 PM?
= 7:15 + 3:30
= 10: 45 PM *Ans.
7. What time was it 3 and 1/2 hours before 7:15 AM?
7:15 - 3:30
Since :15 minutes (7:15) is less than :30 minutes (3:30) you need to borrow an hour to 7 and convert that to minutes. 1 hour = 60 minutes. Now :15 + :60 = 75 minutes.
7:15 is now 6:75
6:75 - 3:30 = 3:45 AM *Ans.
7:15 - 3:30
Since :15 minutes (7:15) is less than :30 minutes (3:30) you need to borrow an hour to 7 and convert that to minutes. 1 hour = 60 minutes. Now :15 + :60 = 75 minutes.
7:15 is now 6:75
6:75 - 3:30 = 3:45 AM *Ans.
8. The fraction 52 / 91 expressed in
lowest term is _____?
52 = 52 / 13
91 91 / 13
= 4 *Ans.
7
52 = 52 / 13
91 91 / 13
= 4 *Ans.
7
9. Car A averages 8 km per liter of
fuel. Car B averages 12 km per liter of fuel. If the price
of fuel is $10 per liter. How much less would a 600 -
km. trip cost for Car A than for Car B?
CAR A :
600 km x $10 = $750
8 km
CAR B :
600 km x $10 = $500
12 km
$750 - $500 = $250 *Ans.
CAR A :
600 km x $10 = $750
8 km
CAR B :
600 km x $10 = $500
12 km
$750 - $500 = $250 *Ans.
Mathematics
Test II Solution - Page 71
10. Change 31/17 to a mixed number.
1
17 / 31
17
14
therefore, the mixed number is 1 14 *Ans.
17
10. Change 31/17 to a mixed number.
1
17 / 31
17
14
therefore, the mixed number is 1 14 *Ans.
17
11. 40 is what part of 64?
Part = 40
64
= 40 / 8
64 / 8
= 5 *Ans.
8
Part = 40
64
= 40 / 8
64 / 8
= 5 *Ans.
8
12. Change 13 3 to
an improper fraction.
7
Just multiply 7 to 13 then add 3 and over it by 7.
7 x 13 = 91 + 3 = 94 / 7 *Ans.
7
Just multiply 7 to 13 then add 3 and over it by 7.
7 x 13 = 91 + 3 = 94 / 7 *Ans.
13. What is the average speed in kph of a car travelling 160
kilometers in 5 hours?
Ave. Speed = distance
time
= 160 km
5 hrs.
= 32 kph *Ans.
Ave. Speed = distance
time
= 160 km
5 hrs.
= 32 kph *Ans.
Mathematics
Test II Solution - Page 72
14. 3 + 1 + 1 = ___________?
4 6 8
= 18 + 4 + 3
24 24 24
= 25
24
= 1 1 *Ans.
24
14. 3 + 1 + 1 = ___________?
4 6 8
= 18 + 4 + 3
24 24 24
= 25
24
= 1 1 *Ans.
24
15. 15 1 - 8 3 = ___________?
3 4
15 and 1/3 is also = 46/3
8 and 3/4 is also = 35/4
= 46 - 35
3 4
= 4(46) - 3(35)
3(4)
= 184 - 105
12
= 79
12
= 6 7 *Ans.
12
16. 8 inches is what part of a foot?
1 FOOT = 12 INCHES
8 inches = 8inches x 1 foot
12 inches
= 8 ft.
12
= 2/3 ft. *Ans.
1 FOOT = 12 INCHES
8 inches = 8
12
= 8 ft.
12
= 2/3 ft. *Ans.
17. If 4 workers can complete 8 identical jobs in 4 days, how long will it take 6
workers to complete 12 such jobs?
k = (4 workers) 4 days
8 jobs
k = 2 workers days
job
No. of days for 12 jobs for 6 workers
N = 2worker days x 12 jobs
job
6 workers
N = 4 days *Ans.
k = (4 workers) 4 days
8 jobs
k = 2 workers days
job
No. of days for 12 jobs for 6 workers
N = 2
N = 4 days *Ans.
Mathematics
Test II Solution - Page 73
18. A bookstore sells two kind of MSA Reviewer Books. "College Admission Test Reviewer (CATR)" and High School Entrance Test Reviewer (HSETR)". If it sells the CATR which yield a profit of $62.00 per book, and it can sell 300 books in a month. It sells the HSETR at a profit of $50.50 per book and it can sell 350 books in one month. Which type of book will yield more profit per month, and by how much?
CATR
Profit = $62 x 300 books
book
= $18,600
HSETR
Profit = $50.50 x 300 books
book
= $17,675
Difference in Profit = $18,600 - $17,675
= $925 *Ans.
therefore the CATR yield $925 more profit than the HSETR
18. A bookstore sells two kind of MSA Reviewer Books. "College Admission Test Reviewer (CATR)" and High School Entrance Test Reviewer (HSETR)". If it sells the CATR which yield a profit of $62.00 per book, and it can sell 300 books in a month. It sells the HSETR at a profit of $50.50 per book and it can sell 350 books in one month. Which type of book will yield more profit per month, and by how much?
CATR
Profit = $62 x 300 books
book
= $18,600
HSETR
Profit = $50.50 x 300 books
book
= $17,675
Difference in Profit = $18,600 - $17,675
= $925 *Ans.
therefore the CATR yield $925 more profit than the HSETR
19. Mr. Jose Suobiron inherited 5/8 of his father's estate. He sold 2/5 of his share. What part of
the entire estate did he sell?
Let x - represents the whole state.
5 x - is the share of Mr. Suobiron
8
N = part of the estate that he sold
N = 5 x 2
8 5
= 10 / 40
= 1/4 of the estate was sold by Mr. Suobiron *Ans.
Let x - represents the whole state.
5 x - is the share of Mr. Suobiron
8
N = part of the estate that he sold
N = 5 x 2
8 5
= 10 / 40
= 1/4 of the estate was sold by Mr. Suobiron *Ans.
20. 13 and 1/3 ounces is what part
of a pound?
16 OUNCES = 1 POUND
= 13 1 ounces x 1 pound
3 ounces
= 40 x 1 pounds
3 16
= 5 / 6 pounds *Ans.
16 OUNCES = 1 POUND
= 13 1 ounces x 1 pound
3 ounces
= 40 x 1 pounds
3 16
= 5 / 6 pounds *Ans.
Mathematics
Test II Solution - Page 74
21. 126 is 3/7 of what number?
3 N = 126
7
N = 126 ( 7 )
3
N = 882 / 3
N = 294 *Ans.
21. 126 is 3/7 of what number?
3 N = 126
7
N = 126 ( 7 )
3
N = 882 / 3
N = 294 *Ans.
22. A roll of ribbon
51 yards long is to be divided into 408 equal parts.
How many inches is the length of each part?
1 YARD = 36 INCHES
N = 51yards x 36 inches ÷ 408 parts
yards
= 51 x 36 x 1 inches/part
408
= 4.5 inches / part *Ans.
1 YARD = 36 INCHES
N = 51
= 51 x 36 x 1 inches/part
408
= 4.5 inches / part *Ans.
23. A water tank is 7/8 full. When
21 liters of water is drawn out, the tank is 5/8 full.
What is the total capacity of the tank in liters?
Let x - be the total capacity of the tank.
7 x - 21 = 5 x
8 8
7 x - 5 x = 21
8 8
2 x = 21
8
1 x = 21
4
x = 21 ( 4 )
1
x = 21(4)
x = 84 *Ans.
Let x - be the total capacity of the tank.
7 x - 21 = 5 x
8 8
7 x - 5 x = 21
8 8
2 x = 21
8
1 x = 21
4
x = 21 ( 4 )
1
x = 21(4)
x = 84 *Ans.
24. A painter completes 2/9 of a job in 3 days. At this
rate, how many more days will it take him to finish the
job?
Let x - be the remaining of days to finish the job.
2 : 3 = 7 : x 7 is part of the job that is unfinished. 1 - 2 = 7
9 9 9 9 9
2 x = 3( 7 )
9 9
2 x = 21
9 9
x = 21 ( 9 )
9 2
x = 21
2
x = 10.5 days *Ans.
Let x - be the remaining of days to finish the job.
2 : 3 = 7 : x 7 is part of the job that is unfinished. 1 - 2 = 7
9 9 9 9 9
2 x = 3( 7 )
9 9
2 x = 21
9 9
x = 21 (
x = 21
2
x = 10.5 days *Ans.
Mathematics
Test II Solution - Page 75
25. A boy spent $320, which was 5/7 of what he had originally. How much did he have originally?
Let x - be the original amount of money that the boy had first.
5 x = $320
7
x = 320 ( 7 )
5
x = $448 *Ans.
25. A boy spent $320, which was 5/7 of what he had originally. How much did he have originally?
Let x - be the original amount of money that the boy had first.
5 x = $320
7
x = 320 ( 7 )
5
x = $448 *Ans.
26. 0.0075 x 1000 = ___________?
To multiply numbers by 10n, move the decimal point of the number to n places to the right.
0.0075 x 1000 = 0.0075 x 103 n = 3 this represents the no. of zero decimals : move the
= 7.5 *Ans decimal point 3 places to the right.
To multiply numbers by 10n, move the decimal point of the number to n places to the right.
0.0075 x 1000 = 0.0075 x 103 n = 3 this represents the no. of zero decimals : move the
= 7.5 *Ans decimal point 3 places to the right.
27. Express 0.572 as a common fraction in lowest term?
0.572 = 527 0.572 - this has 3 decimal places remove the decimal point and
1000 replace it by the denominator of 103 = 1000.
= 572 / 4
1000 / 4
= 143 *Ans.
250
0.572 = 527 0.572 - this has 3 decimal places remove the decimal point and
1000 replace it by the denominator of 103 = 1000.
= 572 / 4
1000 / 4
= 143 *Ans.
250
28. Of the following which is the closest approximation
to the product 0.33 x 0.41 x 0.625 x 0.83 = _____?
0.33 = 1/3
0.41 = 2/5
0.625 = 5/8
0.83 = 5/6
= 1 x 2 x 5 x 5
3 x 5 x 8 x 6
= 50
720
= 5 / 72 *Ans.
0.33 = 1/3
0.41 = 2/5
0.625 = 5/8
0.83 = 5/6
= 1 x 2 x 5 x 5
3 x 5 x 8 x 6
= 50
720
= 5 / 72 *Ans.
Mathematics
Test II Solution - Page 76
29. Dividing by 0.125 is the same as multiplying by _________?
= 1
0.125
1
= 1
8
= 1 x 8
1
= 8 *Ans.
29. Dividing by 0.125 is the same as multiplying by _________?
= 1
0.125
1
= 1
8
= 1 x 8
1
= 8 *Ans.
30. If a copper wire is 3.7 feet
long, its length in inches is ________?
3.7 feet = 3.7 feet x 12 inches
foot
44.4 inches *Ans.
44.4 inches is between 44 and 45
3.7 feet = 3.7 feet x 12 inches
foot
44.4 inches *Ans.
44.4 inches is between 44 and 45
31. 9 =
_________?
0.09 x 0.9
9
= 9 x 9
100 10
9
= 81
1000
= 9 x 1000
81
= 1000 *Ans.
9
0.09 x 0.9
9
= 9 x 9
100 10
9
= 81
1000
= 9 x 1000
81
= 1000 *Ans.
9
32. How much money can be saved by buying 72 pens at $90 per
dozen than buying them for $7.75 each?
Cost in buying by dozen :
= 72pens x 1 dozen x $90
12pens
doz.
= 6 x $90
= $540
Cost in buying per piece :
= 72 x $7.75
= 558
Amount Saved = $558 - $540
= $18 *Ans.
Cost in buying by dozen :
= 72
12
= 6 x $90
= $540
Cost in buying per piece :
= 72 x $7.75
= 558
Amount Saved = $558 - $540
= $18 *Ans.
Mathematics
Test II Solution - Page 77
33. Two countries produce 1/8 and 3/10 respectively of the world production of aluminum. What fraction of the world production do the two nations produce together?
N = 1 + 3
8 10
= 5 + 12
40 40
= 17 *Ans
40
33. Two countries produce 1/8 and 3/10 respectively of the world production of aluminum. What fraction of the world production do the two nations produce together?
N = 1 + 3
8 10
= 5 + 12
40 40
= 17 *Ans
40
34. Of 20 is 25 % of x + 7, then x = ________?
25 % ( x + 7 ) = 20
1/4 ( x + 7 ) = 20
x + 7 = 20 x 4
x + 7 = 80
x = 80 - 7
x = 73 *Ans.
25 % ( x + 7 ) = 20
1/4 ( x + 7 ) = 20
x + 7 = 20 x 4
x + 7 = 80
x = 80 - 7
x = 73 *Ans.
35. If 5 x 5 x Z = 15 x 15 x 15,
then Z = _________?
5 x 5 x Z = 15 x 15 x 15
Z = 15 x 15 x 15
5 x 5
Z = 3 x 3 x 15
Z = 135 *Ans.
5 x 5 x Z = 15 x 15 x 15
Z = 15 x 15 x 15
5 x 5
Z = 3 x 3 x 15
Z = 135 *Ans.
36. The morning class in school begin at 8:05 AM and end at
12:00 noon. There are five class periods of 45 minutes
each with equal intervals between classes. How many
minutes are there in each interval?
Let x - be the length of time of each interval
8: 05 AM + : 45 min-class + x + :45 min-class + x + :45 min-class + x
+ :45 min-class + x + :45 min-class = 12:00
8:05 + 5(45 minutes) + 4x = 12:00
8:05 + 225 minutes + 4x = 12:00
8:05 + 3 hrs & 45 min + 4x = 12:00
11:50 + 4x = 12:00
4x = 10 minutes
x = 10 / 4
x = 2.5 minutes *Ans.
Let x - be the length of time of each interval
8: 05 AM + : 45 min-class + x + :45 min-class + x + :45 min-class + x
+ :45 min-class + x + :45 min-class = 12:00
8:05 + 5(45 minutes) + 4x = 12:00
8:05 + 225 minutes + 4x = 12:00
8:05 + 3 hrs & 45 min + 4x = 12:00
11:50 + 4x = 12:00
4x = 10 minutes
x = 10 / 4
x = 2.5 minutes *Ans.
Mathematics
Test II Solution - Page 78
37. Every seat in a bus was taken and 7 people were standing. At the next stop 15 people got off and 3 got on. How many seats were empty after this stop if everyone was seated?
Let x - be the number of seats
No. of people = x + 7 -15 + 3 No. of empty seats = x - (x - 5)
No. of people = x - 5 No. of empty seats = x - x + 5
No. of seats = 5 *Ans.
37. Every seat in a bus was taken and 7 people were standing. At the next stop 15 people got off and 3 got on. How many seats were empty after this stop if everyone was seated?
Let x - be the number of seats
No. of people = x + 7 -15 + 3 No. of empty seats = x - (x - 5)
No. of people = x - 5 No. of empty seats = x - x + 5
No. of seats = 5 *Ans.
38. A boy scored 134, 145, and 150 in his first 3 games.
What score must he make on his next game
so that his average for the four games will be 149?
x - must be score in the fourth game
x + 134 + 150 + 145 = 149
4
x + 429 = 4 (149)
x + 429 = 596
x = 596 - 429
x = 167 *Ans.
x - must be score in the fourth game
x + 134 + 150 + 145 = 149
4
x + 429 = 4 (149)
x + 429 = 596
x = 596 - 429
x = 167 *Ans.
39. Angelo can type 9 pages in 12 minutes. How many pages
can he type in 8 hours at the same rate?
P - no. of pages :
P x 1 hr = 9 pages
8 hrs 60 mins 12 mins
P = 9
480 12
P = 9 (480)
12
= 9 (40)
360 *Ans.
P - no. of pages :
P x 1 hr = 9 pages
8 hrs 60 mins 12 mins
P = 9
480 12
P = 9 (480)
12
= 9 (40)
360 *Ans.
40. Girlie starts cleaning the yard
at 10 AM and by 11:20, she has finished 4/5 of it. If she continues working at
the same rate, at what time will she finish cleaning the yard?
Time elapse from 10 AM to 11:20 AM is 1 hour and 20 minutes which is = 80 minutes.
4 : 80 minutes = 1 : x
5 5
4 x = 80 ( 1 )
5 5
x = 80 ( 1 ) 5
5 4
= 20 minutes
therefore, 20 minutes after 11:20 AM is 11:40 AM *Ans.
Time elapse from 10 AM to 11:20 AM is 1 hour and 20 minutes which is = 80 minutes.
4 : 80 minutes = 1 : x
5 5
4 x = 80 ( 1 )
5 5
x = 80 ( 1 ) 5
5 4
= 20 minutes
therefore, 20 minutes after 11:20 AM is 11:40 AM *Ans.
Mathematics
Test II Solution - Page 79
41. If 3/8 of a certain number is 2/5, what is 3/4 of that same number?
3 x = 2
8 5
x = 2 ( 8 )
5 3
x = 16
15
3 x = 3 ( 16 )
4 4 15
3 x = 4 *Ans.
4 5
41. If 3/8 of a certain number is 2/5, what is 3/4 of that same number?
3 x = 2
8 5
x = 2 ( 8 )
5 3
x = 16
15
3 x = 3 ( 16 )
4 4 15
3 x = 4 *Ans.
4 5
42. A bus travels 240 kilometers at
60 kph and then returns at 40 kph. What is the average speed in kilometers per
hour for the round trip?
t1 = distance / rate
= 240 km / 60 kph
= 4 hrs.
t2 = distance / rate
= 240 km / 40 kph
= 6 hrs.
rate = total distance
total time
= 240 + 240
4 + 6
= 480
10
= 48 km/hr *Ans.
t1 = distance / rate
= 240 km / 60 kph
= 4 hrs.
t2 = distance / rate
= 240 km / 40 kph
= 6 hrs.
rate = total distance
total time
= 240 + 240
4 + 6
= 480
10
= 48 km/hr *Ans.
43. Mr. Albelda drives his car at the rate
of 60 miles per hour. What is his rate in feet per second?
5280 ft. = 1 mile
rate = 60 mi x 1 hr x 5280 ft
hr 3600 sec 1 mile
= 60 (5280) ft
3600 sec
= 88 ft *Ans.
sec
5280 ft. = 1 mile
rate = 60 mi x 1 hr x 5280 ft
hr 3600 sec 1 mile
= 60 (5280) ft
3600 sec
= 88 ft *Ans.
sec
44. What is 0.05 percent of 6.5
?
= 0.05% x 6.5
= 0.0005 x 6.5
= 0.00325 * Ans.
= 0.05% x 6.5
= 0.0005 x 6.5
= 0.00325 * Ans.
45. At Rosa Alvero Street, in Loyola Heights
8 = 8 / 4
52 52 / 4
= 2 / 13 or 2 : 13 * Ans.
8 = 8 / 4
52 52 / 4
= 2 / 13 or 2 : 13 * Ans.
Mathematics
Test II Solution - Page 80
46. If it takes 16 pipes 10 hours to fill 8 tanks, how long will it take 12 pipes to fill 9 tanks?
Let H be the number of hours
H = (16)(10) pipe - hours x 9
tanks
8tanks 12 pipes
= 16 x 10 x 9
8 x 12
= 1440
96
= 15 hours *Ans.
46. If it takes 16 pipes 10 hours to fill 8 tanks, how long will it take 12 pipes to fill 9 tanks?
Let H be the number of hours
H = (16)(10)
8
= 16 x 10 x 9
8 x 12
= 1440
96
= 15 hours *Ans.
47. Mr. Cruz borrows $360,000. If he
pays back $378,000 after one year, what is his interest rate?
I = F - P
I = $378,000 - $360,000 = 18,000
rate = I x 100%
Pt
= $18,000 x 100%
$360,000
= 5% *Ans.
I = F - P
I = $378,000 - $360,000 = 18,000
rate = I x 100%
Pt
= $18,000 x 100%
$360,000
= 5% *Ans.
48. If 6 men need $3,600 worth of food for a three-day
camping trip, how much will 2 men
need for a 15-day trip?
Let x - be the worth if food needed by 2 men for a 15-day trip
x = $3,600 x (2 x 15 man-days)
6 x 3
= $3,600 x 30
18
= 200 x 30
= $6,000 *Ans.
Let x - be the worth if food needed by 2 men for a 15-day trip
x = $3,600 x (2 x 15 man-days)
6 x 3
= $3,600 x 30
18
= 200 x 30
= $6,000 *Ans.
49. What is 6% of 2.5 ?
6% of 2.5
= 6 x 25
100 10
= 150
1000
= 3 / 20 * Ans.
6% of 2.5
= 6 x 25
100 10
= 150
1000
= 3 / 20 * Ans.
50. What is the value of 60 x 31 x 36 x 7 ?
In this kind of problem we don't need to multiply in order to get the answer. Notice in the choices that the first five digits are all the same so we just have to check what the last digit be This can be done by multiplying the last digit :
0 x 1 x 6 x 7 = 0
Therefore, the answer is : 468, 720 *Ans.
In this kind of problem we don't need to multiply in order to get the answer. Notice in the choices that the first five digits are all the same so we just have to check what the last digit be This can be done by multiplying the last digit :
0 x 1 x 6 x 7 = 0
Therefore, the answer is : 468, 720 *Ans.
Mathematics
Test III Solution - Page 81
Solutions
1. If 9x - 7 = 18y then 9x - 7 = ________?
6
9x - 7 = 18y
9x - 7 = 18y
6 6
= 3y *Ans.
Solutions
1. If 9x - 7 = 18y then 9x - 7 = ________?
6
9x - 7 = 18y
9x - 7 = 18y
6 6
= 3y *Ans.
2. A student buys an MSA Reviewer Book for $175 after
receiving a discount of 12.5%. What was the marked price?
1 MP - 0.125 MP = $175
0.875 MP = $175
7/8 MP = $175 (note : 7/8 is the fraction form of 0.875)
MP = $175 x (8/7)
MP = $200 *Ans.
1 MP - 0.125 MP = $175
0.875 MP = $175
7/8 MP = $175 (note : 7/8 is the fraction form of 0.875)
MP = $175 x (8/7)
MP = $200 *Ans.
3. A town house unit was sold fir
$2.50 M, yielding a 25% profit. For how much would it
be sold to yield only a 10% profit on the cost?
Let C be the original cost of the house
Let 0.25C be the profit
C + 0.25C = $2.5 M
1.25C = $2.5M
1.25C = $2.5M
1.25 1.25
C = $2M
The new selling price that would yield at 10% profit on the cost would be :
= $2M + 0.10 ($2M)
= $2M + 0.20M
= $2.2M *Ans.
Let C be the original cost of the house
Let 0.25C be the profit
C + 0.25C = $2.5 M
1.25C = $2.5M
1.25C = $2.5M
1.25 1.25
C = $2M
The new selling price that would yield at 10% profit on the cost would be :
= $2M + 0.10 ($2M)
= $2M + 0.20M
= $2.2M *Ans.
4. What single discount is equivalent to successive
discounts if 5% and 10%?
The formula for a single rate of discount equivalent to the series of discounts is :
R = 1 - [(1 - r1) (1 - r2)...(1 - rn)]
for r1 = 5% and r2 = 10%
R = 1 - [(1 - 0.05) (1 - 0.10)]
= 1 - [(0.95) (0.90)]
= 1 - 0.855
= 0.145 or 14.5% *Ans.
The formula for a single rate of discount equivalent to the series of discounts is :
R = 1 - [(1 - r1) (1 - r2)...(1 - rn)]
for r1 = 5% and r2 = 10%
R = 1 - [(1 - 0.05) (1 - 0.10)]
= 1 - [(0.95) (0.90)]
= 1 - 0.855
= 0.145 or 14.5% *Ans.
5. How many miles are there in 40
kilometers?
1 mile = 1.6 kilometers
40 kilometers = 40km x 1 mile
1.6km
= 25 miles *Ans.
1 mile = 1.6 kilometers
40 kilometers = 40
1.6
= 25 miles *Ans.
Mathematics
Test III Solution - Page 82
6. If water tank can be filled 1 and 3/4 hours. What part of the tank can be filled in exactly 1 hour?
The part of the tank that can be filled in 1 hour is 1 + 1 and 3/4
= 1 ÷ 7
4
= 1 x 4
7
= 4 *Ans.
7
6. If water tank can be filled 1 and 3/4 hours. What part of the tank can be filled in exactly 1 hour?
The part of the tank that can be filled in 1 hour is 1 + 1 and 3/4
= 1 ÷ 7
4
= 1 x 4
7
= 4 *Ans.
7
7. If 5 items cost d dollars how much would x items cost at
the same rate?
The cost of x items = d x
5
= dx *Ans.
5
The cost of x items = d x
5
= dx *Ans.
5
8. In a group of 8, 000 applicants
for a civil service examination, 1600 failed to take
the first part of the test. What percent of the total
applicants took the first part of the test?
Rate = 8000 - 1600 x 100%
8000
= 6400 x 100%
8000
= 0.8 x 100%
= 80% *Ans.
Rate = 8000 - 1600 x 100%
8000
= 6400 x 100%
8000
= 0.8 x 100%
= 80% *Ans.
9. If the ratio a : b is 11 : 9,
then a + b is ________?
The sum of a and b can't be determined from the given information because there are infinite possibilities for this like;
a + b = 11 + 9
= 22 + 18
= 33 + 27 and so on...
d. can't be determined from the given information. *Ans.
The sum of a and b can't be determined from the given information because there are infinite possibilities for this like;
a + b = 11 + 9
= 22 + 18
= 33 + 27 and so on...
d. can't be determined from the given information. *Ans.
Mathematics
Test III Solution - Page 83
10. If 4 men can paint a fence in 2 days, what part of the job can be completed by one man in 8 days?
1 whole job x 1man x 8 days
4men x 2 days
8 whole jobs
8
1 whole job *Ans.
10. If 4 men can paint a fence in 2 days, what part of the job can be completed by one man in 8 days?
1 whole job x 1
4
8 whole jobs
8
1 whole job *Ans.
11. Of John's salary, 1/10 is spent
for clothing, and 1/4 for board and lodging. What part of the salary is left
for other expenditures and savings?
Let x - be the part left.
x = 1 - ( 1 + 1 )
10 4
= 1 - (2 + 5)
20
= 20 - 7
20 20
= 13 / 20 *Ans.
Let x - be the part left.
x = 1 - ( 1 + 1 )
10 4
= 1 - (2 + 5)
20
= 20 - 7
20 20
= 13 / 20 *Ans.
12. Which of the following fractions
is closest to 1/3 ?
We can solve the problem by getting the LCM of the given fraction and all the chioces.
The LCM = 15 then compare the differences of each choice to 1/3.
1/3 - 1/5 = 5/15 - 3/15 = 2/15
2/5 - 1/3 = 6/15 - 5/15 = 1/5 *Ans.
2/3 - 1/3 = 10/15 - 5/15 = 10/15
3/5 - 1/3 = 9/15 - 5/15 = 4/15
We can solve the problem by getting the LCM of the given fraction and all the chioces.
The LCM = 15 then compare the differences of each choice to 1/3.
1/3 - 1/5 = 5/15 - 3/15 = 2/15
2/5 - 1/3 = 6/15 - 5/15 = 1/5 *Ans.
2/3 - 1/3 = 10/15 - 5/15 = 10/15
3/5 - 1/3 = 9/15 - 5/15 = 4/15
13. Write 0.5 % as decimal.
To change % to decimal, we drop the % sign and move the decimal point two places to the left.
0.05 % = 0.005 *Ans.
To change % to decimal, we drop the % sign and move the decimal point two places to the left.
0.05 % = 0.005 *Ans.
Mathematics
Test III Solution - Page 84
14. If 10 parts of alcohol is mixed with 15 parts of water, what part of the mixture is alcohol ?
The part of the mixture is alcohol = 10
10 + 15
= 10
25
= 2/5 *Ans.
14. If 10 parts of alcohol is mixed with 15 parts of water, what part of the mixture is alcohol ?
The part of the mixture is alcohol = 10
10 + 15
= 10
25
= 2/5 *Ans.
15. If 2/5 of the workers in a
factory go on vacation is September and 1/3 of the remainder take their vacation in
October, what fraction of the workers take their
vacation in some other time?
The fraction of the workers that take their vacation in some other time
= 1 - [ 2 + 1 (1 - 2 )]
5 3 5
= 1 - [ 2 + 1 ( 3 )]
5 3 5
= 1 - [ 2 + 1 ]
5 5
= 1 - 3
5
= 2 *Ans.
5
The fraction of the workers that take their vacation in some other time
= 1 - [ 2 + 1 (1 - 2 )]
5 3 5
= 1 - [ 2 + 1 ( 3 )]
5 3 5
= 1 - [ 2 + 1 ]
5 5
= 1 - 3
5
= 2 *Ans.
5
16. A bill was passed by a vote of 7 : 5 . What part of the
vote counts were in favor of the bill?
The part of the vote in favor of the bill : 7
7 + 5
= 7 / 12 *Ans.
The part of the vote in favor of the bill : 7
7 + 5
= 7 / 12 *Ans.
17. If a man travels for half of an hour at 60 km/hr, and
for quarter of an hour for 120 km/hr, what is his
average speed?
d1/2 = 1 hr. x 60 km = 30 km
2 hr
d1/4 = 1 hr. x 120 km = 30 km
4 hr
Average speed = total distance
total time
( 30 + 30 )
( 1 + 1 )
2 4
( 30 + 30 ) km.
3 hr.
4
60 ( 4 ) kph
3
Ave. Speed = 80 kph. *Ans.
d1/2 = 1 hr. x 60 km = 30 km
2 hr
d1/4 = 1 hr. x 120 km = 30 km
4 hr
Average speed = total distance
total time
( 30 + 30 )
( 1 + 1 )
2 4
( 30 + 30 ) km.
3 hr.
4
60 ( 4 ) kph
3
Ave. Speed = 80 kph. *Ans.
Mathematics
Test III Solution - Page 85
18. What part of an hour elapses between 9:52 AM and 10:16 AM ?
= 10:16 - 9:52
10:16 is also equal to 9:76 since 76 is equal to 1 hour and 16 minutes. 9 hours + 1 hour and 16 minutes = 10:16.
= 9:76 - 9:52 = 24 minutes
= 24minutes x 1 hr
60min
= 24 / 60 hrs.
= 2 / 5 hours *Ans.
18. What part of an hour elapses between 9:52 AM and 10:16 AM ?
= 10:16 - 9:52
10:16 is also equal to 9:76 since 76 is equal to 1 hour and 16 minutes. 9 hours + 1 hour and 16 minutes = 10:16.
= 9:76 - 9:52 = 24 minutes
= 24
60
= 24 / 60 hrs.
= 2 / 5 hours *Ans.
19. If the ratio of boys to girls is
3 : 7 . If the class has 40 students, how many additional boys are needed to enroll to make the ratio 2
: 1 ?
3x + 7x = 40 The number of boys : 3x = 3(4) = 12
10x = 40 The number of girls : 7x = 7(4) = 28
x = 40 since the desired ratio of boys to girls
10 is 2 : 1 .
x = 4 the required number of boys is 2 x 28 = 56
so 56 - 12 = 44 more boys are needed. *Ans.
3x + 7x = 40 The number of boys : 3x = 3(4) = 12
10x = 40 The number of girls : 7x = 7(4) = 28
x = 40 since the desired ratio of boys to girls
10 is 2 : 1 .
x = 4 the required number of boys is 2 x 28 = 56
so 56 - 12 = 44 more boys are needed. *Ans.
20. If 45 feet of uniform wire weigh
5 kilograms, what is the weight of 30 yards
o the same wire ?
Let x - be the length of 30 yards of the same wire.
30 yards x 3 feet = 90 feet
yard
x = 5
90 45
x = 1
90 9
x = 10 kgs. *Ans.
Let x - be the length of 30 yards of the same wire.
30 yards x 3 feet = 90 feet
yard
x = 5
90 45
x = 1
90 9
x = 10 kgs. *Ans.
21. A school has enough oatmeal
to feed 15 children in 4 days. If 5 more children are added,
how many days will the oatmeal last ?
This problem is an example of an inverse proportion.
4 : 1/5 = x : 1 / (15 + 5)
4 : 1/15 = x : 1/20
1 x = 4 ( 1 )
15 20
x = 1
15 5
x = 1 (15)
5
x = 3 days *Ans.
This problem is an example of an inverse proportion.
4 : 1/5 = x : 1 / (15 + 5)
4 : 1/15 = x : 1/20
1 x = 4 ( 1 )
15 20
x = 1
15 5
x = 1 (15)
5
x = 3 days *Ans.
Mathematics
Test III Solution - Page 86
22. If a car can travel 60 km on 12 liters of gasoline, how many liters will be needed in a 210 km trip ?
This is a direct proportion problem, Let x - be the number of liters needed.
x : 210 = 12 : 60
60x = 210 (12)
60x = 2520
x = 2520 / 60
x = 42 liters *Ans.
22. If a car can travel 60 km on 12 liters of gasoline, how many liters will be needed in a 210 km trip ?
This is a direct proportion problem, Let x - be the number of liters needed.
x : 210 = 12 : 60
60x = 210 (12)
60x = 2520
x = 2520 / 60
x = 42 liters *Ans.
23. Write 7.5% as a fraction.
7.5% = 7.5
100
= 75
100
= 3 *Ans.
40
7.5% = 7.5
100
= 75
100
= 3 *Ans.
40
24. Write 3/8 % as decimal.
3/8 % = 0.375 %
= 0.00375 *Ans.
3/8 % = 0.375 %
= 0.00375 *Ans.
25. Find 40% of 60.
= 0.40 x 60
= 24 *Ans.
= 0.40 x 60
= 24 *Ans.
27. What is 175% of 24 ?
P = Rate x Base
= 1.75 x 24
= 42 *Ans.
P = Rate x Base
= 1.75 x 24
= 42 *Ans.
28. What percent of 60 is 42 ?
R = P x 100%
B
R = 70% *Ans.
R = P x 100%
B
R = 70% *Ans.
29. 54 is 20% of what number ?
N = 54 ÷ 0.20
= 540 / 2
= 270 *Ans.
N = 54 ÷ 0.20
= 540 / 2
= 270 *Ans.
30. 24 is 150% of what number ?
24 = 1.5 x N
N = 24 / 1.5
N = 240 / 15
N = 16 *Ans.
24 = 1.5 x N
N = 24 / 1.5
N = 240 / 15
N = 16 *Ans.
Mathematics
Test III Solution - Page 88
31. How many thirty- seconds are there in 62 ½ % ?
N = 62 ½ %
32
N = 5
32 8
N = 5 (32)
8
N = 20 *Ans.
31. How many thirty- seconds are there in 62 ½ % ?
N = 62 ½ %
32
N = 5
32 8
N = 5 (32)
8
N = 20 *Ans.
32. A shirt marked $560 is sold for $392. What was the rate of discount ?
Rate = discount x 100%
original price
= $560 - $392 x 100 %
$560
= $168 x 100%
$560
= 30% *Ans.
Rate = discount x 100%
original price
= $560 - $392 x 100 %
$560
= $168 x 100%
$560
= 30% *Ans.
33. A kinder class has g number of
girls and b number of boys. The ratio of boys to girls
is _____ ?
The ratio of boys to girls is b / g *Ans.
The ratio of boys to girls is b / g *Ans.
______
34. / 1 + 1 = _________ ?
√ 25 144
_________
= / 144 + 25
√ 25 144
_________
= / 169
√ (25 ) (144)
34. / 1 + 1 = _________ ?
√ 25 144
_________
= / 144 + 25
√ 25 144
_________
= / 169
√ (25 ) (144)
= 13
(5 ) (12)
= 13 / 60 *Ans.
Mathematics
Test III Solution - Page 89
35. A basketball team has won 24 games out of 36 games played. It has 24 more games to play. How many ofthese must the team win to make its record 80% for the season ?
The total number of wins = 80% x (total no. of games played)
= 0.80 x ( 36 + 24 )
= 0.80 ( 60 )
= 48
Since they already won 24 games, they need to win 24 more games. * Ans.
35. A basketball team has won 24 games out of 36 games played. It has 24 more games to play. How many ofthese must the team win to make its record 80% for the season ?
The total number of wins = 80% x (total no. of games played)
= 0.80 x ( 36 + 24 )
= 0.80 ( 60 )
= 48
Since they already won 24 games, they need to win 24 more games. * Ans.
36. If prices are reduced by 25% sales increased by
33 ⅓ % what is the net effect on gross revenue ?
Revenue = price x no. items sold
R = P x N
Rorig = PN
If prices are reduced by 25%
Rnew = ( P - 25% P) ( N + 33 ⅓ N )
= ( P - ¼ P ) ( N + ⅓ N )
= ( ¾ P ) ( 4/3 N )
Rnew = PN
Rnew = Rorig
The revenues remain the same * Ans.
Revenue = price x no. items sold
R = P x N
Rorig = PN
If prices are reduced by 25%
Rnew = ( P - 25% P) ( N + 33 ⅓ N )
= ( P - ¼ P ) ( N + ⅓ N )
= ( ¾ P ) ( 4/3 N )
Rnew = PN
Rnew = Rorig
The revenues remain the same * Ans.
37. An 8-meter rope is cut so that one part is 3/5 of the
other. How long in meters, is the shorter segment ?
Let x - be the length of the shorter rope.
Let 8 - x be the length of the larger rope
x = 3 ( 8 - x )
5
5x = 3 ( 8 - x )
5x = 24 - 3x
5x + 3x = 24
8x = 24
x = 3 meters * Ans.
Let x - be the length of the shorter rope.
Let 8 - x be the length of the larger rope
x = 3 ( 8 - x )
5
5x = 3 ( 8 - x )
5x = 24 - 3x
5x + 3x = 24
8x = 24
x = 3 meters * Ans.
38. When the gasoline guage of an automobile shows 1/8 full,
52.5 liters is needed to
completely fill the gasoline tank. What is the capacity, in liters of the
gasoline tank?
Let x - be the capacity in liters
x - 1 x = 52.5
2
7 x = 52.5
8
x = 52.5 ( 8 )
7
x = 60 * Ans.
Let x - be the capacity in liters
x - 1 x = 52.5
2
7 x = 52.5
8
x = 52.5 ( 8 )
7
x = 60 * Ans.
Mathematics
Test III Solution - Page 90
39. What part of gallon is 7 pints, given that 1 quart = 2 pints, 4 quarts = 1 gal. ?
therefore, 8 pints = 1 gal.
7 pints = 7 pints x 1 gal
8 pints
= 7 / 8 gallon * Ans.
39. What part of gallon is 7 pints, given that 1 quart = 2 pints, 4 quarts = 1 gal. ?
therefore, 8 pints = 1 gal.
7 pints = 7 pints x 1 gal
8 pints
= 7 / 8 gallon * Ans.
40. If 7 is added to four times a number, the result is 91.
What is the number ?
Let x - be the number.
4x + 7 = 91
4x = 91 - 7
4x = 84
x = 84 / 4
x = 21 * Ans.
Let x - be the number.
4x + 7 = 91
4x = 91 - 7
4x = 84
x = 84 / 4
x = 21 * Ans.
41. The area of a square is 36 sq. cm. What is the perimeter
of the square ?
A = s2
36 = s2
_____
s = √ 36
s = 6 cm.
P = 4s
= 4 (6 cm.)
= 24 cm. * Ans.
A = s2
36 = s2
_____
s = √ 36
s = 6 cm.
P = 4s
= 4 (6 cm.)
= 24 cm. * Ans.
42. A truck can carry a load of 8 / 9 tons. How many trips
must the truck make to deliver 10 and 2 / 3 tons of sand?
Let N - be the number of trips.
N = 10 ⅔ ÷ 8/9
= 32 ÷ 8
3 9
= 32 x 9
3 8
= 12 trips * Ans.
Let N - be the number of trips.
N = 10 ⅔ ÷ 8/9
= 32 ÷ 8
3 9
= 32 x 9
3 8
= 12 trips * Ans.
Mathematics
Test III Solution - Page 91
43. What is the value of
6a2b3
______ if a = 2 and b = 3 ?
9
6a2b3
= ______
9
6(2)2(3)3
= ________
9
6(4)(27)
= ________
9
= 72 * Ans.
43. What is the value of
6a2b3
______ if a = 2 and b = 3 ?
9
6a2b3
= ______
9
6(2)2(3)3
= ________
9
6(4)(27)
= ________
9
= 72 * Ans.
44. Z + 4 = 4
Z
This problem can be solved the easiest way by substituting each choice to Z.
Z = 1
1 + 4 = 4
1
1 + 4 = 4
5 ≠ 4
Z = 2
2 + 4 = 4
2
2 + 2 = 4
4 = 4 * Ans.
Z
This problem can be solved the easiest way by substituting each choice to Z.
Z = 1
1 + 4 = 4
1
1 + 4 = 4
5 ≠ 4
Z = 2
2 + 4 = 4
2
2 + 2 = 4
4 = 4 * Ans.
45. 1 ÷ 1 =
_________ ?
x 1
x
= 1 • x
x 1
= 1 * Ans.
x 1
x
= 1 • x
x 1
= 1 * Ans.
______
46. x √0.0004 = 4 : x = _______ ?
x (0.02) = 4
x = 4
0.02
x = 400
2
x = 200 * Ans.
46. x √0.0004 = 4 : x = _______ ?
x (0.02) = 4
x = 4
0.02
x = 400
2
x = 200 * Ans.
Mathematics
Test III Solution - Page 92
47. A piece of wire is cut into three, so that the first is three times as long as the second and the second is three times as long as the third. What part of the entire piece is the shortest?
First part = 9x
Second part = 3x
Third part = x
9x + 3x + x = 13x
part = length of the shortest part
length of entire wire
= x
13x
= 1 / 13 * Ans.
47. A piece of wire is cut into three, so that the first is three times as long as the second and the second is three times as long as the third. What part of the entire piece is the shortest?
First part = 9x
Second part = 3x
Third part = x
9x + 3x + x = 13x
part = length of the shortest part
length of entire wire
= x
13x
= 1 / 13 * Ans.
48. What is the average of the first 20 positive integers ?
Average = sum of the numbers
numbers of items added
= 1 + 2 + + 3 + 4 + 5 + 6 + 7 .... + 20
20
= 10.5 * Ans.
Average = sum of the numbers
numbers of items added
= 1 + 2 + + 3 + 4 + 5 + 6 + 7 .... + 20
20
= 10.5 * Ans.
49. A sales representative earns 5% commission on all sales between $ 20, 000 and $ 60,
000, and 8% on all sales over $ 60,000. What is the commission in a week in
which her total sales was $ 80, 000 ?
Commission = 5% (6000) + 8% (80,000 - 60,000)
= 0.05 (60,000) + 0.08 (20,000)
= 3,000 + 1,600
= $ 4, 600 * Ans.
Commission = 5% (6000) + 8% (80,000 - 60,000)
= 0.05 (60,000) + 0.08 (20,000)
= 3,000 + 1,600
= $ 4, 600 * Ans.
_________
50. / 12 + 12
√ 27 9
_________
/ 4 + 4
√ 9 3
_________
/ 4 + 12
√ 9
50. / 12 + 12
√ 27 9
_________
/ 4 + 4
√ 9 3
_________
/ 4 + 12
√ 9
_____
/ 16
√ 9
= 4 / 3 * Ans.
/ 16
√ 9
= 4 / 3 * Ans.
Mathematics
Test IV Solution - Page 93
Solutions
1. A car that cost $ 1.2 M can be sold for $ 600, 000 after 5 years of use. What will be the yearly depreciation cost ?
Yearly depreciation cost = depreciation
no. of years
= $ 1,200,000 - $ 600,000
5
= $ 600,000
5
= $ 120, 000 per year * Ans.
Solutions
1. A car that cost $ 1.2 M can be sold for $ 600, 000 after 5 years of use. What will be the yearly depreciation cost ?
Yearly depreciation cost = depreciation
no. of years
= $ 1,200,000 - $ 600,000
5
= $ 600,000
5
= $ 120, 000 per year * Ans.
2. How many times does the digit 7 appear in the numbers
from 1 to 100 ?
7, 17, 27, 37, 47, 57, 67, 77, 87, 97,
71, 72, 73, 74, 75, 76, 77, 78, 79
19 times * Ans.
7, 17, 27, 37, 47, 57, 67, 77, 87, 97,
71, 72, 73, 74, 75, 76, 77, 78, 79
19 times * Ans.
3. At the rate of $ 44 per hundred
sheets of colored bond paper, how much
is the cost of 500 sheets ?
Cost of the 550 sheets = $ 44 x 550 sheets
100 sheets
= $ 44 x 5.5
= $ 242 * Ans.
Cost of the 550 sheets = $ 44 x 550 sheets
100 sheets
= $ 44 x 5.5
= $ 242 * Ans.
4. At $ 25 per board foot of wood, what is the cost of 15
pieces of 2" x 2" x 12' ?
( 1 board foot = 1 ft. x 1 ft. x 1 inch )
Cost = $ 25 x 2" x 2" x 12" bd. ft.
bd. ft. 12"
= $ 1, 500 * Ans.
( 1 board foot = 1 ft. x 1 ft. x 1 inch )
Cost = $ 25 x 2" x 2" x 12" bd. ft.
bd. ft. 12"
= $ 1, 500 * Ans.
5. The decimal form of 0.56 % is
__________ ?
Move 2 decimal places to the left (100%).
0.56 % = 0.0056 * Ans.
Move 2 decimal places to the left (100%).
0.56 % = 0.0056 * Ans.
Mathematics
Test IV Solution - Page 94
6. If 3 feet = 1 yard, how many yards are there in 27 feet ?
3 feet : 1 yard = 27 feet : x yard
3 : 1 = 27 : x
3x = 1(27)
3x = 27
x = 27 / 3
x = 9 yards * Ans.
6. If 3 feet = 1 yard, how many yards are there in 27 feet ?
3 feet : 1 yard = 27 feet : x yard
3 : 1 = 27 : x
3x = 1(27)
3x = 27
x = 27 / 3
x = 9 yards * Ans.
7. How many feet are there in 9 and 1/3 yards ?
Given that 1 yard = 3 feet :
1 yard : 3 feet = 9 ⅓ yards : x feet
1 : 3 = 9 ⅓ : x
1(x) = 3(9 ⅓)
x = 3 (28/3)
x = 28 feet * Ans.
Given that 1 yard = 3 feet :
1 yard : 3 feet = 9 ⅓ yards : x feet
1 : 3 = 9 ⅓ : x
1(x) = 3(9 ⅓)
x = 3 (28/3)
x = 28 feet * Ans.
8. A hand-carved wooden dining set
is priced at $69, 950. If 20% discount is given to the customer, how much would he have to pay for the set ?
Net Price = $ 69, 950 - 20 ($69,950)
= $ 69, 950 - $13,390
= $ 55, 960 * Ans.
Net Price = $ 69, 950 - 20 ($69,950)
= $ 69, 950 - $13,390
= $ 55, 960 * Ans.
9. If an article priced at $99.80 is
subjected to a 10% VAT, what would be the total amount to be paid
for the article ?
Total Amount to be paid = $ 99.80 + 0.10 ($99.80)
= $ 99.80 + $ 9.98
= $ 109.78 * Ans.
Total Amount to be paid = $ 99.80 + 0.10 ($99.80)
= $ 99.80 + $ 9.98
= $ 109.78 * Ans.
10. Find the cost of 6 and 1/2 dozen eggs at $ 30.00 per
dozen.
1 dozen : $ 30.00 = 6 and 1/2 dozens : x dollars
1 : 30 = 6.5 : x
1(x) = 30 (6.5)
x = $ 195.00 * Ans.
1 dozen : $ 30.00 = 6 and 1/2 dozens : x dollars
1 : 30 = 6.5 : x
1(x) = 30 (6.5)
x = $ 195.00 * Ans.
Mathematics
Test IV Solution - Page 95
11. A lady employee purchased an umbrella for $ 180 less 20%. How much should she pay if its is subject to a 5 % sales tax ?
Total Amount = ($180 - 0.20 x $ 180) x (1.05)
to be paid
= ($180 - 36) (1.05)
= $144 x 1.05
= $ 151.20 * Ans
11. A lady employee purchased an umbrella for $ 180 less 20%. How much should she pay if its is subject to a 5 % sales tax ?
Total Amount = ($180 - 0.20 x $ 180) x (1.05)
to be paid
= ($180 - 36) (1.05)
= $144 x 1.05
= $ 151.20 * Ans
12. Mr. Mansueto Velasco Jr. is buying a piece of lot at
Filinvest Homes East. The dimension of the rectangular
lot is 14 meters by 30 meters at $ 3, 500 per square meters, what would be the
total cost of the lot ?
Total Cost = area x price per unit area
of the lot
= (14 x 30) sq. meters x $ 3, 500
sq. meters
= 14 x 30 x $3,500
= $ 1, 470, 000 * Ans.
Total Cost = area x price per unit area
of the lot
= (14 x 30) sq. meters x $ 3, 500
sq. meters
= 14 x 30 x $3,500
= $ 1, 470, 000 * Ans.
13. How much must a salesman sell in a month to yield him a
commission of $ 12, 000, if his rate of commission is 5% on goods sold ?
Sales = Commission / Rate
= $ 12, 000 / 0.05
= $ 240, 000 * Ans.
Sales = Commission / Rate
= $ 12, 000 / 0.05
= $ 240, 000 * Ans.
14. How much would Charlie receive from his monthly salary of $ 8,000 after deducting 2 and 1/2 % for SSS contribution and 5% withholding tax ?
Total Rate of deductions = 2 ½ % + 5 % = 7 ½ %
Net Pay = Regular pay ( 1 - rate of deductions )
= $ 8, 000 ( 1 - 0.075 )
= $ 8, 000 ( 0.925 )
= $ 7, 400 * Ans.
Total Rate of deductions = 2 ½ % + 5 % = 7 ½ %
Net Pay = Regular pay ( 1 - rate of deductions )
= $ 8, 000 ( 1 - 0.075 )
= $ 8, 000 ( 0.925 )
= $ 7, 400 * Ans.
Mathematics
Test IV Solution - Page 96
15. A student had $ 1, 050 in his wallet. He spent $ 640 for books and school supplies. What part of his money did he spend?
Part of the money spent = $ 630 / $ 210
$ 1050 / $ 210
= 3 / 5 * Ans.
15. A student had $ 1, 050 in his wallet. He spent $ 640 for books and school supplies. What part of his money did he spend?
Part of the money spent = $ 630 / $ 210
$ 1050 / $ 210
= 3 / 5 * Ans.
16. MS. Cecille Garcia saves 18% of her monthly
salary of $ 16, 500. How much does she saved in
a year?
Amount of money saved = 0.18 x $ 16, 500 x 12 month
month
year
= 0.18 x $ 16, 500 x 12
= $ 35, 640 * Ans.
Amount of money saved = 0.18 x $ 16, 500 x 12
= 0.18 x $ 16, 500 x 12
= $ 35, 640 * Ans.
17. Mrs. Leny Ngo wishes to buy a second hand car, the cash
price of which is $ 150, 000. Not having ready cash she agrees to pay 1/3 down
and the balance in 10 monthly installments of 11, 000
each. What is the total price of the car ?
Total price of the car = ⅓ x $ 150, 000 + 10 x $ 11, 000
= $ 50, 000 + $ 110, 000
= $ 160, 000 * Ans.
Total price of the car = ⅓ x $ 150, 000 + 10 x $ 11, 000
= $ 50, 000 + $ 110, 000
= $ 160, 000 * Ans.
18. A cross-stitch store owner buys
cross-stitch frame at $ 12, 500 each. How much should
he sell each in order to realize a profit of 3/20 more
than the buying price ?
Selling price = $ 12, 500 x ( 1 + 3 )
20
= $ 12, 500 ( 23 )
20
= $ 14, 375 * Ans.
Selling price = $ 12, 500 x ( 1 + 3 )
20
= $ 12, 500 ( 23 )
20
= $ 14, 375 * Ans.
Mathematics
Test IV Solution - Page 97
19. This year XYZ company's profit was $ 2, 440, 000, which is 22% more than last year's profit. How much was the profit last year ?
Let x - be the year's profit
x + 0.22x = $ 2, 440, 000
1.22x = $ 2, 440, 000
x = $ 2, 440, 000
1.22
x = $ 2, 000, 000 * Ans
19. This year XYZ company's profit was $ 2, 440, 000, which is 22% more than last year's profit. How much was the profit last year ?
Let x - be the year's profit
x + 0.22x = $ 2, 440, 000
1.22x = $ 2, 440, 000
x = $ 2, 440, 000
1.22
x = $ 2, 000, 000 * Ans
20. Mrs. Ramos pays $ 1, 530 for a dress at 15 % discount.
How much is the marked price ?
Let x - be the marked price
Marked price - Discount = Selling price
x - 0.15 x = $ 1530
0.85x = $ 1530
x = $ 1540
0.85
x = $ 1, 800 * Ans.
Let x - be the marked price
Marked price - Discount = Selling price
x - 0.15 x = $ 1530
0.85x = $ 1530
x = $ 1540
0.85
x = $ 1, 800 * Ans.
21. A customer buys 4 pairs of socks
originally priced at $ 60.00 each. If the reduced price
is $ 47.50, how much does he save on this purchase ?
Amount saved = 4 x ( $ 60.00 - $ 47.50)
= 4 x $ 12.50
= $ 50.00 * Ans.
Amount saved = 4 x ( $ 60.00 - $ 47.50)
= 4 x $ 12.50
= $ 50.00 * Ans.
22. Gerard left City A to drive to
City B at 6:15 A.M. and arrived at 1:45 P.M. If he averaged 60 km per hour and
stopped one hour for lunch, how far is City A to City B ?
No. of hours :
6 : 15 to 11:45
1:45 PM - 6:15 PM
13:45 PM - 6:15 PM = 7:30 or 7 and 1/2 hours total time
total time traveled = 7 ½ hours - 1 hour (time spent for lunch) = 6 ½ hours.
distance = rate x time
60 = km x 6 ½ hours
hr
= (60 x 6 ½ ) km
= [60 x 6 + 60 ½ ] km
= 360 + 30
= 390 km * Ans.
No. of hours :
6 : 15 to 11:45
1:45 PM - 6:15 PM
13:45 PM - 6:15 PM = 7:30 or 7 and 1/2 hours total time
total time traveled = 7 ½ hours - 1 hour (time spent for lunch) = 6 ½ hours.
distance = rate x time
60 = km x 6 ½ hours
hr
= (60 x 6 ½ ) km
= [60 x 6 + 60 ½ ] km
= 360 + 30
= 390 km * Ans.
Mathematics
Test IV Solution - Page 98
____ _____
23. The sum of √ 81 + √ 100 is ________ ?
square root of 81 is 9 and
square root of 100 is 10
therefore, 9 + 10 = 19 * Ans.
____ _____
23. The sum of √ 81 + √ 100 is ________ ?
square root of 81 is 9 and
square root of 100 is 10
therefore, 9 + 10 = 19 * Ans.
24. The sum of three consecutive integers
is 54. Find the smallest integer.
Let x - be the first consecutive integer
Let x + 1 be the second consecutive integer
Let x + 2 be the third consecutive integer
x + (x + 1) + (x + 2) = 54
3x + 3 = 54
3x = 54 - 3
3x = 51
x = 51 / 3
x = 17 * Ans.
Let x - be the first consecutive integer
Let x + 1 be the second consecutive integer
Let x + 2 be the third consecutive integer
x + (x + 1) + (x + 2) = 54
3x + 3 = 54
3x = 54 - 3
3x = 51
x = 51 / 3
x = 17 * Ans.
25. How many miles does a car travel
if it averages at a rate of 35 miles per hour for 3
hours and 24 minutes?
time = 3 hrs and 24 min
= 3 hrs + 24 / 60 hr.
= 3 and ⅖ hrs.
distance = rate x time
= 35 miles x 3 ⅖ hrs
hr
= (35 x 3 ⅖) miles
= (35 x 3) + (35 + ⅖) miles
= [105 + 14] miles
= 119 miles * Ans.
time = 3 hrs and 24 min
= 3 hrs + 24 / 60 hr.
= 3 and ⅖ hrs.
distance = rate x time
= 35 miles x 3 ⅖ hrs
hr
= (35 x 3 ⅖) miles
= (35 x 3) + (35 + ⅖) miles
= [105 + 14] miles
= 119 miles * Ans.
26. Elmer can deliver newspaper in his route for 1 ½ hours.
Wowie who takes his place one day finds that it takes him 1 ½ longer
to deliver these. How long will it take to deliver the papers
if they work together ?
In one hour,
Elmer can do 1 = 1 = 2 of the job
1 3 3
Wowie can do 1 = 1 of the job
1 ½ + 1 ½ 3
(Part of the job finished in 1 hr.) x
(no. of hours) = 1 whole job
( ⅔ + ⅓ ) x N = 1
3 x N = 1
3
1 x N = 1
N = 1 hour * Ans.
In one hour,
Elmer can do 1 = 1 = 2 of the job
1 3 3
Wowie can do 1 = 1 of the job
1 ½ + 1 ½ 3
(Part of the job finished in 1 hr.) x
(no. of hours) = 1 whole job
( ⅔ + ⅓ ) x N = 1
3 x N = 1
3
1 x N = 1
N = 1 hour * Ans.
Mathematics
Test IV Solution - Page 99
27. If it takes h hours to paint the wall, what part of the wall is painted in one hour ?
part of the wall painted in 1 hour = 1 / h * Ans.
27. If it takes h hours to paint the wall, what part of the wall is painted in one hour ?
part of the wall painted in 1 hour = 1 / h * Ans.
28. A sock of corn will feed 18 ducks for 54 days. How long will it feed 12 ducks ?
* This is an example of an inverse proportion problem. As the number of ducks decreases the number of days increases.
N : 1 = 54 : 1
12 18
N( 1 ) = 1 (54)
18 12
27 3
N = 1 x54 x 18 days
12
2
N = 81 days * Ans.
* This is an example of an inverse proportion problem. As the number of ducks decreases the number of days increases.
N : 1 = 54 : 1
12 18
N( 1 ) = 1 (54)
18 12
27 3
N = 1 x
2
N = 81 days * Ans.
29. Find the next number in the series 1,
4, 9, 16, _____ ?
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25 * Ans.
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25 * Ans.
30. A bag is sold for $680 while marked at $800. What was
the rate of the discount ?
rate of discount = discount x 100 %
marked price
= 800 - 680 x 100%
800
= 120 x 100%
800
= 15 % * Ans.
rate of discount = discount x 100 %
marked price
= 800 - 680 x 100%
800
= 120 x 100%
800
= 15 % * Ans.
31. Six hundred examinees passed the
Licensure Examination last year. This represents the 8
⅓ percent of the total examinees. How many examinees failed the exam?
let F - be the number of examinees who failed
8 ⅓ % : 600 = ( 100 - 8 ⅓ ) % : F
1 : 600 = 11 : F
12 12
1 F = 11 ( 600 )
12 12
F = 6, 600 * Ans.
let F - be the number of examinees who failed
8 ⅓ % : 600 = ( 100 - 8 ⅓ ) % : F
1 : 600 = 11 : F
12 12
1 F = 11 ( 600 )
12 12
F = 6, 600 * Ans.
Mathematics
Test IV Solution - Page 100
32. If 4 miles = 6.44 km, then 14.49 km equals how many miles ?
4 miles : 6.44 km = x miles : 14.49 km
4 : 6.44 = x : 14.49
6.44x = 4 (14.49)
6.44x = 57.96
x = 57.96 / 6.44
x = 9 miles * Ans.
32. If 4 miles = 6.44 km, then 14.49 km equals how many miles ?
4 miles : 6.44 km = x miles : 14.49 km
4 : 6.44 = x : 14.49
6.44x = 4 (14.49)
6.44x = 57.96
x = 57.96 / 6.44
x = 9 miles * Ans.
33. (a2 - 4b2)
c is equivalent to ac + _________ ?
(a + 2b)
= (a + 2b) (a - 2b) x c
(a + 2b)
= (a - 2b) x c
= ac - 2bc
= ac + (-2bc) * Ans.
(a + 2b)
= (a + 2b) (a - 2b) x c
(a + 2b)
= (a - 2b) x c
= ac - 2bc
= ac + (-2bc) * Ans.
34. In a certain class the ratio of boys to girls is 4 : 5. If the class has 54 students, how many are girls ?
Girls = 5 / 9 (total number of students)
= (5 / 9) 54
= 30 girls * Ans.
Girls = 5 / 9 (total number of students)
= (5 / 9) 54
= 30 girls * Ans.
35. Solve for x :
ax = bx + cx - d, a ≠ b ≠ c.
d = bx + cx - ax
d = x (b + c - a)
x = d
(b + c - a)
x = d * Ans
b + c – a
ax = bx + cx - d, a ≠ b ≠ c.
d = bx + cx - ax
d = x (b + c - a)
x = d
(b + c - a)
x = d * Ans
b + c – a
Mathematics
Test IV Solution - Page 101
36. The ratio of men athlete to women in an athletic meet is 5 : 3 and the total number of athlete is 2, 400, how many additional women athlete would have to join to make the ratio of men to women 1 : 1 ?
Original number of men;
( 5 / 8 ) x 2, 400 = 1, 500
Original number of women;
( 3 / 8 ) x 2, 400 = 900
To make the number of women equal to the number of men we must add ( 1500 - 900 ).
therefore, 600 women is needed. * Ans.
36. The ratio of men athlete to women in an athletic meet is 5 : 3 and the total number of athlete is 2, 400, how many additional women athlete would have to join to make the ratio of men to women 1 : 1 ?
Original number of men;
( 5 / 8 ) x 2, 400 = 1, 500
Original number of women;
( 3 / 8 ) x 2, 400 = 900
To make the number of women equal to the number of men we must add ( 1500 - 900 ).
therefore, 600 women is needed. * Ans.
37. If prices are reduced by 20 %, quantity sold increase by 25 %. What is the net effect on the gross
revenue?
Revenue = (price) x (Quantity sold)
Rold = pq
Rnew = (p - 0.20p) x (q x 0.25q)
= (0.80p)(1.25) pq
= (0.80)(1.25) pq
= 1 pq
Rnew = Rold
therefore, the revenue remains the same * Ans.
Revenue = (price) x (Quantity sold)
Rold = pq
Rnew = (p - 0.20p) x (q x 0.25q)
= (0.80p)(1.25) pq
= (0.80)(1.25) pq
= 1 pq
Rnew = Rold
therefore, the revenue remains the same * Ans.
38. The average of three numbers is xyz. If the sum of two
numbers is x + y, what is the other number?
Sum of the items added = average
no. of items added
x + y + (other number) = xyz
3
3[ x + y + (other number) = xyz ] 3
3
x + y + other number = 3 xyz
other number = 3 xyz - (x + y) * Ans.
Sum of the items added = average
no. of items added
x + y + (other number) = xyz
3
x + y + other number = 3 xyz
other number = 3 xyz - (x + y) * Ans.
Mathematics
Test IV Solution - Page 102
39. When + 13 is added to - 15, the sum is _______ ?
Sum = +13 + (-15)
Sum = -2 * Ans.
39. When + 13 is added to - 15, the sum is _______ ?
Sum = +13 + (-15)
Sum = -2 * Ans.
40. When -15 is subtracted from
-18, the difference is _______?
Difference = -18 - (-15)
Difference = -18 + 15
Difference = -3 * Ans.
Difference = -18 - (-15)
Difference = -18 + 15
Difference = -3 * Ans.
41. When the product of (-4) and
(-17) is divided by 2, the quotient is _____ ?
Product = (-4) (-17)
2
= 68 / 2
= 34 * Ans.
Product = (-4) (-17)
2
= 68 / 2
= 34 * Ans.
42. If 5x + 17 = 32, then x = _________ ?
5x + 17 = 32
5x = 32 - 17
5x = 15
x = 15 / 5
x = 3 * Ans.
5x + 17 = 32
5x = 32 - 17
5x = 15
x = 15 / 5
x = 3 * Ans.
43. Solve for M :
M - M = 4
7 3
3M - 7M = 4
21 21
-4M = 4
21
M =4 ( -21 )
4
M = -21 * Ans.
M - M = 4
7 3
3M - 7M = 4
21 21
-4M = 4
21
M =
M = -21 * Ans.
Mathematics
Test IV Solution - Page 103
44. If x + y = 4a and x - y = 2b then y = ______ ?
x + y = 4a -------> x = 4a - y
x - y = 2b -------> x = 2b + y
x = x
2b + y = 4a - y
y + y = 4a - 2b
2y = 4a - 2b
2y = 4a - 2b
2 2
y =4a - 2b
2
y = 2a - b * Ans.
44. If x + y = 4a and x - y = 2b then y = ______ ?
x + y = 4a -------> x = 4a - y
x - y = 2b -------> x = 2b + y
x = x
2b + y = 4a - y
y + y = 4a - 2b
2y = 4a - 2b
y =
y = 2a - b * Ans.
45. If 0.37 m = 0.0111 then m = _____ ?
m = 0.0111
0.37
= 11.1
37
= 0.3 * Ans
m = 0.0111
0.37
= 11.1
37
= 0.3 * Ans
46. If 1 / M = 4 and S = 2, what is S in terms
of M ?
Since S = 2
4 = 1
M
2 (2) = 1
M
2 S = 1
M
S = 1
2M * Ans.
Since S = 2
4 = 1
M
2 (2) = 1
M
2 S = 1
M
S = 1
2M * Ans.
Mathematics
Test IV Solution - Page 104
47. A horse is tied to a pole with a rope of 7 meters long. How much grazing area does it have?
(use π = 22 / 7).
Area = π r2
= π (7m)2
= 22 (49m2)
7
= 22 (7m2)
= 154m2 * Ans.
47. A horse is tied to a pole with a rope of 7 meters long. How much grazing area does it have?
(use π = 22 / 7).
Area = π r2
= π (7m)2
= 22 (
= 22 (7m2)
= 154m2 * Ans.
48. What number is missing in this sequence : 5, 7, 11, 17,
________ ?
5 + 2 = 7
7 + 4 = 11
11 + 6 = 17
17 + 8 = 25
therefore, 25 is the * Ans.
5 + 2 = 7
7 + 4 = 11
11 + 6 = 17
17 + 8 = 25
therefore, 25 is the * Ans.
49. How many two-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 if a digit cannot be used more than
once?
5 - the five numbers can be used
4 - only four of the numbers can be used since repetition of the digits is not allowed
5 x 4 = 20
therefore, 20 numbers * Ans.
5 - the five numbers can be used
4 - only four of the numbers can be used since repetition of the digits is not allowed
5 x 4 = 20
therefore, 20 numbers * Ans.
50. What is the value of x in 5 : x = x : 125 ?
5 : x = x : 125
x (x) = 5 (125)
x2 = 625
_____
x = √ 625
x = 25 * Ans.
5 : x = x : 125
x (x) = 5 (125)
x2 = 625
_____
x = √ 625
x = 25 * Ans.
51. If one bilao of pansit guisado serves 7 people, how many
bilaos are needed to serve a banquet of 126 people?
N = no. of bilaos needed to serve 126 people
N : 126 = 1 : 7
N (7) = 126 (1)
7N = 126
N = 126 / 7
N = 18 * Ans.
N = no. of bilaos needed to serve 126 people
N : 126 = 1 : 7
N (7) = 126 (1)
7N = 126
N = 126 / 7
N = 18 * Ans.
Mathematics
Test V Solution - Page 105
Solutions
1. What number is as much more than 8 as it is less than 32 ?
Let x - be the number
x - 8 = 32 - x
x + x = 32 +8
2x = 40
x = 40 / 2
x = 20 * Ans.
Solutions
1. What number is as much more than 8 as it is less than 32 ?
Let x - be the number
x - 8 = 32 - x
x + x = 32 +8
2x = 40
x = 40 / 2
x = 20 * Ans.
2. A container van that is 3 meters wide, 5 meters long and
4 meters high will transport 200 crates whose volume is 6 cubic
meters. How many trips will it take to transport all the crates?
Let N - be the number of trips
No. of trips = (No. of crates) x volume x 1 trip
crate volume of the van
N = 200crates x 6
m3 x 1 trip
crate
(3 x 5 x 4)m3
N = (200) (6)
3 x 4 x 5
N = 1200
60
N = 20 trips * Ans.
Let N - be the number of trips
No. of trips = (No. of crates) x volume x 1 trip
crate volume of the van
N = 200
N = (200) (6)
3 x 4 x 5
N = 1200
60
N = 20 trips * Ans.
3. A rectangular block of copper, with dimensions 4m x 6m x
9m, is melted and recast into a cubical block. Find the
length of the side of the cubical block.
Vcubical block = Vrectangular block
S3 = (4 x 6 x 9) m3
S3 = 216 m3
______
S = ∛216 m3
S = 6m * Ans.
Vcubical block = Vrectangular block
S3 = (4 x 6 x 9) m3
S3 = 216 m3
______
S = ∛216 m3
S = 6m * Ans.
4. There are 9 male teachers for
every 14 female teachers. If there are 69 teachers in all, how many teachers
are female?
9 : 14 = Male : Female
23 69
No. of Female teachers = (69 / 23) x 14
= 3 x 14
= 42 * Ans.
9 : 14 = Male : Female
23 69
No. of Female teachers = (69 / 23) x 14
= 3 x 14
= 42 * Ans.
___
5. What would be the closest approximation to√ 66 ?
___
√ 64 = 8
___
√ 66 ≅ 8.1 * Ans.
5. What would be the closest approximation to√ 66 ?
___
√ 64 = 8
___
√ 66 ≅ 8.1 * Ans.
Mathematics
Test V Solution - Page 106
6. Manny can do a certain job in 1 day, Anna can do the same job in 2 days, and Josie can do the job in 3 days. How many days will it take them to do the job if they work together?
One 1 day Manny can finish the whole job
Anna can finish 1/2 of the same job
Josie can finish 1/3 of the same job
Let N - be the days that it takes to finish the job if they work together.
( 1 + 1 + 1 ) N = 1
1 2 3
( 6 + 3 + 2 ) N = 1
6
11 N = 1
6
N = 1 x 6 (reciprocal of 11 / 6)
11
N = 6 / 11 day * Ans.
6. Manny can do a certain job in 1 day, Anna can do the same job in 2 days, and Josie can do the job in 3 days. How many days will it take them to do the job if they work together?
One 1 day Manny can finish the whole job
Anna can finish 1/2 of the same job
Josie can finish 1/3 of the same job
Let N - be the days that it takes to finish the job if they work together.
( 1 + 1 + 1 ) N = 1
1 2 3
( 6 + 3 + 2 ) N = 1
6
11 N = 1
6
N = 1 x 6 (reciprocal of 11 / 6)
11
N = 6 / 11 day * Ans.
7. In the figure, all the line
segments meet at right angles and each segments has a
length of 1 unit. What is the area of the figure in square units?
8. If x - 3 = y, then (y - x )3 =
_____ ?If x - 3 = y;
-3 = y - x
(-3)3 = (y - x)3
-27 = (y - 3)3 * Ans.
9. A speed of 90 km per hour is equivalent to how many
meters per second?
= 90 km x 1 hr x 1000 m
hr 3600 sec km
= 90 x 1000 m
3600 hr
= 25 m * Ans.
sec
= 90 km x 1 hr x 1000 m
hr 3600 sec km
= 90 x 1000 m
3600 hr
= 25 m * Ans.
sec
10. A rectangular sheet of cardboard 5 inches long and 4 inches wide is cut into squares
one inch on a side. What is the maximum number of such
squares that can be formed? 
Mathematics
Test V Solution - Page 107
11. A housewife bought 3 kilograms of beef priced at $ 108.75 per kilogram. How much change did she receive from a five-hundred dollar bill?
Change = $ 500 - (3 x $ 108.75)
= $ 500 - $ 326.25
= $ 173.75 * Ans.
Mathematics
Test V Solution - Page 10711. A housewife bought 3 kilograms of beef priced at $ 108.75 per kilogram. How much change did she receive from a five-hundred dollar bill?
Change = $ 500 - (3 x $ 108.75)
= $ 500 - $ 326.25
= $ 173.75 * Ans.
12. A delivery of 480 baskets of mangoes is divided into two
fruit stands so that the difference between the two
orders is 1/3 their average. What is the ratio of the
smaller to the larger amount?
Let x - be the no. of baskets in the fruit stand.
Let 480 - x be the number in the second fruit stand.
(480 - x) - x = 1 (x + y) ------> 480 - 2x = 80
3 2 ------> 2x = 480 - 80
------> 2x = 400
but x + y = 480 1 ( 480 ) ------> x = 200 480 - x = 280
since the total 3 2
delivery = 480
The ratio is 200 : 280 = 5 : 7 * Ans.
40 40
Let x - be the no. of baskets in the fruit stand.
Let 480 - x be the number in the second fruit stand.
(480 - x) - x = 1 (x + y) ------> 480 - 2x = 80
3 2 ------> 2x = 480 - 80
------> 2x = 400
but x + y = 480 1 ( 480 ) ------> x = 200 480 - x = 280
since the total 3 2
delivery = 480
The ratio is 200 : 280 = 5 : 7 * Ans.
40 40
13. When the first and the last digits
of 2, 836 are interchanged, the new number is ________.
6,832 -----> the new number
6,832 - 2836 = 3996
therefore, the new number is 3,996 more than 2,836 * Ans.
6,832 -----> the new number
6,832 - 2836 = 3996
therefore, the new number is 3,996 more than 2,836 * Ans.
14. If twice the value of a certain number is increased by 8
the result is 40. What is the number?
Let x - be the number
2x + 8 = 40
2x = 40 -8
2x = 32
x = 32 / 2
x = 16 * Ans
Let x - be the number
2x + 8 = 40
2x = 40 -8
2x = 32
x = 32 / 2
x = 16 * Ans
15. In a group of 120 persons, there are 32 more women than
men. How many women are there in the group?
Let x - be the number of women
Let x - 32 be the number of men
x + ( x - 32 ) = 120
2x - 32 = 120
2x = 120 + 32
2x = 152
x = 152 / 2
x = 76 women * Ans.
Let x - be the number of women
Let x - 32 be the number of men
x + ( x - 32 ) = 120
2x - 32 = 120
2x = 120 + 32
2x = 152
x = 152 / 2
x = 76 women * Ans.
Mathematics
Test V Solution - Page 108
16. If the dimensions of a square change in such a manner that the area remains constant, what must happen to the other side if one side will be increased by 1/4 of itself?
16. If the dimensions of a square change in such a manner that the area remains constant, what must happen to the other side if one side will be increased by 1/4 of itself?
(s + 1 s) y = s (s)4
5 ( s )( y )= s2
4
y = s2 ( 4 )
5s
y = 4 s
5
s = - 4 s = 1 s
5 5
therefore, it decreased by 1/5 of itself * Ans.
17. A man rowed 4 miles upstream for 2 hours. If the river
flowed with a current of 2 miles per hour, how long did the man's
return trip take?
Let x - be the rate of the boat in still water
Let 2x - be the rate of the boat upstream
Let 2 mph - be the rate of the current
Let (x + 2) - speed of the boat downstream
rateup x time = distance
(x - 2) (2) = 4
2x - 4 = 4
2x = 4 + 4
2x = 8
x = 4 miles / hr
ratedown x time = distance
(x+2) (time) = 4
(4+2) (time) = 4
6 (time) = 4
time = 4 / 6
time = 2 / 3 hrs. * Ans.
Let x - be the rate of the boat in still water
Let 2x - be the rate of the boat upstream
Let 2 mph - be the rate of the current
Let (x + 2) - speed of the boat downstream
rateup x time = distance
(x - 2) (2) = 4
2x - 4 = 4
2x = 4 + 4
2x = 8
x = 4 miles / hr
ratedown x time = distance
(x+2) (time) = 4
(4+2) (time) = 4
6 (time) = 4
time = 4 / 6
time = 2 / 3 hrs. * Ans.
18. The rectangle shown in the figure is divided into 6 equal squares. If the perimeter
of the rectangle is 42 cm, what is the area of each square in cm2 ?
14x = 42
x = 42 / 14
x = 3 cm.
Area of the squares = x2
= (3 cm)2
= 9
cm2 * Ans.
Mathematics
Test V Solution - Page 109
19. If the area of the rectangle ABCD shown below is 36 square units, how many square units is the area of the shaded region?
19. If the area of the rectangle ABCD shown below is 36 square units, how many square units is the area of the shaded region?
Arectangle = bh
Arectangle = 36
bh = 36
Atriangle = 1/2 bh
= 1/2 (36)
= 18 sq. units * Ans.
Arectangle = 36
bh = 36
Atriangle = 1/2 bh
= 1/2 (36)
= 18 sq. units * Ans.
20. This tank holds 48 liters of
gasoline and the car averages 5 kilometers per liter. Approximately how many
kilometers can a car travel this given guage?
The guage indicates that the tank is 1/4 full.
Let N - be the number of kilometers that can be traveled.
N = ( 1 tank) x 48 liters
x 5 km
4
tank
liter
= 1/4 x 48 x 5 km
= 60 km. * Ans
21. Which of the following graphs represents the taxi rates for a company that charges $ 3.50 for the first 200
meters and $ 1.00 for each additional 100 meters?
This is the approximate graph for the taxi rate, there is an abrupt change in the fare for every 100 meters change in the distance.
This is the approximate graph for the taxi rate, there is an abrupt change in the fare for every 100 meters change in the distance.
22. A laboratory assistant was
preparing a solution that should have included 40 milligrams
of chemical. If he actually used 41.30 milligrams, what was his percentage
error (to the nearest 0.01 %)?
% error = error x 100%
correct value
= 41.30 - 40 x 100%
40
= 1.3 %
40
= 130 %
40
= 3.25 % * Ans
% error = error x 100%
correct value
= 41.30 - 40 x 100%
40
= 1.3 %
40
= 130 %
40
= 3.25 % * Ans
Mathematics
Test V Solution - Page 110
23. Menthol drops come in packs of 8 for $ 3.60. Butterballs come in packs of 6 for $ 2.25. Aida bought 48 pieces of candy. How many of each kind of candy did she buy, if she spent $ 19.80?
b. 3 packs of Menthol drops and 4 packs of Butterballs.
= (3 x $ 3.60) + (4 x $2.25)
= $ 10.80 + $ 9.00
= $ 19.80 * Ans.
23. Menthol drops come in packs of 8 for $ 3.60. Butterballs come in packs of 6 for $ 2.25. Aida bought 48 pieces of candy. How many of each kind of candy did she buy, if she spent $ 19.80?
b. 3 packs of Menthol drops and 4 packs of Butterballs.
= (3 x $ 3.60) + (4 x $2.25)
= $ 10.80 + $ 9.00
= $ 19.80 * Ans.
Use the following table for questions 23 and 24.
24. How much tax is due on a taxable income of $65, 000?
Tax due = $6, 075 + 0.19 ($65,000 - $60,000)
= $6, 075 + 0.19 ($5,000)
= $6, 075 + $950
Tax due = $7, 025 * Ans.
Tax due = $6, 075 + 0.19 ($65,000 - $60,000)
= $6, 075 + 0.19 ($5,000)
= $6, 075 + $950
Tax due = $7, 025 * Ans.
25. How much tax is due on a taxable income of $55, 000?
Tax due = $3, 075 + 0.15 ($55,000 - $40,000)
= $3, 075 + 0.15 ($15,000)
= $3, 075 + $2,250
Tax due = $5, 325 * Ans.
Tax due = $3, 075 + 0.15 ($55,000 - $40,000)
= $3, 075 + 0.15 ($15,000)
= $3, 075 + $2,250
Tax due = $5, 325 * Ans.
Mathematics
Test V Solution - Page 111
26. Anabelle paid $ 19, 675 tax. If x was her income, which of the following statements is TRUE?
b. $ 19, 675 tax due belongs to this range * Ans.
Over $ 100, 000 but not over $ 250, 000
$ 13, 675 + 24% of excess over $ 100, 000
therefore, Anabelle's income is between $ 100,000 and $ 250,000
26. Anabelle paid $ 19, 675 tax. If x was her income, which of the following statements is TRUE?
b. $ 19, 675 tax due belongs to this range * Ans.
Over $ 100, 000 but not over $ 250, 000
$ 13, 675 + 24% of excess over $ 100, 000
therefore, Anabelle's income is between $ 100,000 and $ 250,000
27. Mang Pablo decided to keep a record of the
money he collects from his newspaper route.
Using the information given, how much money does Mang
Pablo collect in the month of February? (Note : Assume
that February has 28 days and the February 1 was on a Sunday).
* Ans - Total $ 9, 990
28. If 10 soldiers can survive for 12 days in 15 packs of
rations, how many packs will be needed for 8 men to
survive for 18 days?
Let N - be the number of packs
N packs -----> 15 packs ---> N = 15 x (8 x 18) packs
8 men x 18 days 10 men x 12 days 10 x 12
N = 18 packs * Ans.
Let N - be the number of packs
N packs -----> 15 packs ---> N = 15 x (8 x 18) packs
8 men x 18 days 10 men x 12 days 10 x 12
N = 18 packs * Ans.
29. If it takes Victor twice as long to earn $ 600 as it
takes Warnen to earn $ 400, what is the ratio of
Victor's per day to Warnen's pay per day?
Warnen earns 400 in x days
Victor earns 600 in 2x days
Therefore he earns 300 in 2x days
The ratio of Victor's pay to
Warnen's pay in x days is 400 : 300 or 4 : 3 * Ans
Warnen earns 400 in x days
Victor earns 600 in 2x days
Therefore he earns 300 in 2x days
The ratio of Victor's pay to
Warnen's pay in x days is 400 : 300 or 4 : 3 * Ans
30. What is the cost of fuel for a 120-km trip by car?
Cost of fuel = 120 km x $ 500 ---->
120 x $ 5 -----> $ 600 *Ans.
100 km
31. If the total wages of a bus driver for 100-km trip is $ 970, and the only cost for a bus
are the fuel and the driver's wage. How
much should a bus company charge to charter a
bus with a driver for a 200-km trip in order to obtain 50% more than the cost?
Cost for a 100-km trip = Cfuel + Cdrives ------> 875 + 970 ------> $ 1,845
Total Cost = ( $ 1, 845 x 200 km ) x 1.50 ------> $ 5, 535 * Ans.
100 km
Cost for a 100-km trip = Cfuel + Cdrives ------> 875 + 970 ------> $ 1,845
Total Cost = ( $ 1, 845 x 200 km ) x 1.50 ------> $ 5, 535 * Ans.
100 km
32. If 5 buses, 9 cars, 4 motorcycles
make a 100-km trip. What is the average fuel cost per vehicle?
Average Cost = total cost of fuel ----> (5 x $ 875) + (9 x $ 500) + (4 x $ 175)
total no. of vehicle 5 + 9 + 4
$ 4375 + $ 4500 + $ 700 ------> $ 9575 ----> $ 531.94 * Ans
5 + 9 + 4 18
Average Cost = total cost of fuel ----> (5 x $ 875) + (9 x $ 500) + (4 x $ 175)
total no. of vehicle 5 + 9 + 4
$ 4375 + $ 4500 + $ 700 ------> $ 9575 ----> $ 531.94 * Ans
5 + 9 + 4 18
33. A store owner bought 2 dozen cans of corned beef at $ 30
each. He sold two-thirds of them at 25% profit but was
forced to take a 30% loss on the rest. What was his total profit (or loss) on
the item?
Total Selling Price
= [ 2 (24 cars) x $ 30 x ( 1 + 0.25 )] + [ 1 (24 cars x $ 30 ) ( 1 - 0.30 )]
3 car 3 car
= [ 2 (24) x $ 30( 1.25 )] + [ 1 (24)($ 30)(0.70)]
3 3
Total Selling Price = $ 600 + $ 168
= $ 768
Total cost = $30 x 24 cars = $720
car
Gain = Total selling price - Total cost
= $ 768 - $ 720
= $ 48 * Ans.
Total Selling Price
= [ 2 (24 cars) x $ 30 x ( 1 + 0.25 )] + [ 1 (24 cars x $ 30 ) ( 1 - 0.30 )]
3 car 3 car
= [ 2 (24) x $ 30( 1.25 )] + [ 1 (24)($ 30)(0.70)]
3 3
Total Selling Price = $ 600 + $ 168
= $ 768
Total cost = $30 x 24 cars = $720
car
Gain = Total selling price - Total cost
= $ 768 - $ 720
= $ 48 * Ans.
34. The cost of x purchasing grams of Salad A, y grams of
Salad B and z grams of Salad C will be _____.
Cost of Salad A = $ 200 x x gm x 100¢ = 25x ¢
100 gm P 1,000
Cost of Salad B = $ 30 x y gm x 100¢ = 30y ¢
100 gm P 1,000
Cost of Salad C = $ 35 x z gm x 100¢ = 35z ¢
100 gm P 1,000
therefore, the total cost is (25x + 30y + 35z) cents * Ans.
Cost of Salad A = $ 200 x x gm x 100¢ = 25x ¢
100 gm P 1,000
Cost of Salad B = $ 30 x y gm x 100¢ = 30y ¢
100 gm P 1,000
Cost of Salad C = $ 35 x z gm x 100¢ = 35z ¢
100 gm P 1,000
therefore, the total cost is (25x + 30y + 35z) cents * Ans.
35. Which of the following diets would supply the most grams
of vitamins?
c. Salad A + 50g Salad B + (300 g) Salad C
c. Salad A + 50g Salad B + (300 g) Salad C
= 0.40 (200) + 0.30 (100) + 0.50 (200) ----> 80 + 30 +
100 ----> 210 gms * Ans.
36. All of the following diets would supply at least 85
grams of carbohydrates. Which of the diets costs the
least?
b. $ 25 (3) + $ 30 (1) + $ 35 (2)
$ 75 + $ 30 + $ 70 = $ 175 * Ans.
b. $ 25 (3) + $ 30 (1) + $ 35 (2)
$ 75 + $ 30 + $ 70 = $ 175 * Ans.
Mathematics
Test V Solution - Page 114
37. If jackfruits are twice as expensive as watermelons, and watermelon is one-third as expensive as durians. What is the ratio of the price of one jackfruit to one durian?
Let x - be the cost of watermelon
Let 2x - be the cost of the jackfruit
Let 3x - be the cost of the durian
= Jackfruit : Durian
= 2x : 3x
= 2 : 3 * Ans.
37. If jackfruits are twice as expensive as watermelons, and watermelon is one-third as expensive as durians. What is the ratio of the price of one jackfruit to one durian?
Let x - be the cost of watermelon
Let 2x - be the cost of the jackfruit
Let 3x - be the cost of the durian
= Jackfruit : Durian
= 2x : 3x
= 2 : 3 * Ans.
38. A retailer buys a pack of sugar from Uniwide Sales for $
459. He then marks up the price by 1/3 and sells it at
a discount of 16 2/3 %. What was his profit in this
item?
Marked price = $ 459 + 1/3 ($ 459) ----------> 459 + $ 153 -------> $ 612
Discounted Price = $ 612 - 16 % ($ 612) ---------> $ 612 - 1/6 ($ 612) ------> $ 510
Profit = Selling Price - Cost
= $ 510 - $ 459
= $ 51 * Ans.
Marked price = $ 459 + 1/3 ($ 459) ----------> 459 + $ 153 -------> $ 612
Discounted Price = $ 612 - 16 % ($ 612) ---------> $ 612 - 1/6 ($ 612) ------> $ 510
Profit = Selling Price - Cost
= $ 510 - $ 459
= $ 51 * Ans.
39. Forrest Gump walks down the road for 30 minutes at a rate of 3 MPH. He waits 10
minutes for a bus, which brings his back to his starting point at 4 : 25. If he begun his walk at 3 : 35 the
same afternoon, what was the average speed on the bus?
dwalked = rate x time
= 3 mi. x 1 hr. ------> dwalked = 1.5 miles
hr. 2
timetravelled by the bus = 4:25 - 3:35 - :30 - :10 ------> 10 mins ----> 1/6 hr.
speedof the bus = distance --------> 1.5 minutes ---> (1.5 x 6) mi/hr ---> 9 mi/hr * Ans.
time 1/6 hr
dwalked = rate x time
= 3 mi. x 1 hr. ------> dwalked = 1.5 miles
hr. 2
timetravelled by the bus = 4:25 - 3:35 - :30 - :10 ------> 10 mins ----> 1/6 hr.
speedof the bus = distance --------> 1.5 minutes ---> (1.5 x 6) mi/hr ---> 9 mi/hr * Ans.
time 1/6 hr
40. Miss Felisa Gascon had $ 2 million to invest. She
invested part of it at 4% a year and the remainder at
5% per year. After one year she earned $ 95, 000 in interest. How much of the
original investment was placed at 5% rate?
Let x - be the amount of invested at 5%
Let 2,000,000 - x be the amount invested at 4%
0.05x + 0.04 (2,000,000 - x) = 95000
0.05x + 80000 - 0.04x = 95000
0.01x = 95000 - 80000
0.01x = 15000
x = 15000 / 0.01
x = 1, 500, 000 * Ans.
Let x - be the amount of invested at 5%
Let 2,000,000 - x be the amount invested at 4%
0.05x + 0.04 (2,000,000 - x) = 95000
0.05x + 80000 - 0.04x = 95000
0.01x = 95000 - 80000
0.01x = 15000
x = 15000 / 0.01
x = 1, 500, 000 * Ans.
Mathematics
Test V Solution - Page 115
41. Which of the following is NOT a possible remainder if a positive integer is divided 5?
The possible remainders are 0, 1, 2, 3, 4,
therefore, 5 is not a possible remainder * Ans.
41. Which of the following is NOT a possible remainder if a positive integer is divided 5?
The possible remainders are 0, 1, 2, 3, 4,
therefore, 5 is not a possible remainder * Ans.
42. In a buidling plan, 1/4 cm
represents 2 meters. If the main entrance is supposed to be 8 meters wide, how
wide would its representation be on the plan?
Let N - be the representation of the plan
1/4 : 2 = N : 8
2N = (1/4) (8)
2N = 8/4
2N = 2
N = 2/2
N = 1 cm. * Ans.
Let N - be the representation of the plan
1/4 : 2 = N : 8
2N = (1/4) (8)
2N = 8/4
2N = 2
N = 2/2
N = 1 cm. * Ans.
43. A real state agent marks a certain property up 30% above
the original cost. Then he gives a client
a 15% discount. If the final selling
price of the property was $8.619 M, what was the original cost of the
property?
Let x - be the original cost
(x + 0.30x) ( 1 - 0.15) = $8.619 M
(1.30x) (0.85) = $8.619 M
1.105x = $8.619 M
x = $8.619 M / 1.105
x = 7.8 M * Ans.
Let x - be the original cost
(x + 0.30x) ( 1 - 0.15) = $8.619 M
(1.30x) (0.85) = $8.619 M
1.105x = $8.619 M
x = $8.619 M / 1.105
x = 7.8 M * Ans.
44. If 2/3 the perimeter of a square is 16, then what is the
length of one of its sides?
2/3 P = 16
P = 16 (3/2)
P = 48/2
P = 24
Perimeter formula for SQUARE is P = 4S.
P = 4S
24 = 4S
24 = 4S
24/4 = S
6 = S
therefore, S = 6 * Ans.
2/3 P = 16
P = 16 (3/2)
P = 48/2
P = 24
Perimeter formula for SQUARE is P = 4S.
P = 4S
24 = 4S
24 = 4S
24/4 = S
6 = S
therefore, S = 6 * Ans.
45. What values of x can satisfy the equation
(3x + 6) (2x - 8) = 0 ?
3x + 6 = 0
3x = -6
x = -6 / 3
x = - 2
2x - 8 = 0
2x = 8
x = 8 / 2
x = 4 * Ans.
3x + 6 = 0
3x = -6
x = -6 / 3
x = - 2
2x - 8 = 0
2x = 8
x = 8 / 2
x = 4 * Ans.
Mathematics
Test V Solution - Page 116
46. If 8 men can plant 288 trees in one day, how many trees can 12 men plant in 5 days?
Let N - be the number of trees
N = 288 trees x 12 men x 5 days -----> 288 x 12 x 5
8 men - 1 day 8 trees
N = 2, 160 trees * Ans.
46. If 8 men can plant 288 trees in one day, how many trees can 12 men plant in 5 days?
Let N - be the number of trees
N = 288 trees x 12 men x 5 days -----> 288 x 12 x 5
8 men - 1 day 8 trees
N = 2, 160 trees * Ans.
47. If the length of a rectangle is increased by 25% and its width is decreased by 20%, what happens to the area of the triangle?
Aorig. = LW
Anew = L (1+0.25) x W (1 - 0.20)
= L (1.25) x W (0.8) -----> (1.25) (0.8) LW
Anew = 1 x LW
Anew = Aorig.
therefore, no change in the area * Ans.
48. The formula for the volume of a sphere is V = 4/3 πr3. If the radius (r) is
tripled, what will be the ratio of the new volume to the original volume?
Vorig. = 4/3 πr3
Vnew = 4/3 π(3r)3 -----> = 4/3 π(27r3) ------> 27 (4/3 πr3)
Vnew = 27 Vorig. -----> Vnew : Vorig. = 27 : 1 * Ans.
Vorig. = 4/3 πr3
Vnew = 4/3 π(3r)3 -----> = 4/3 π(27r3) ------> 27 (4/3 πr3)
Vnew = 27 Vorig. -----> Vnew : Vorig. = 27 : 1 * Ans.
49. The scale on a map is 1 : 8. If a surveyor
reads a certain measurement on the map as 4.6 cm
instead of 5.0 cm, what will be the resulting approximate percent error on the full size model?
% error = error x 100% -> 5.0 - 4.6 x 100% -> 0.4 x 100% -> 8% *Ans.
correct value 5.0 5
% error = error x 100% -> 5.0 - 4.6 x 100% -> 0.4 x 100% -> 8% *Ans.
correct value 5.0 5
50. In a certain recipe, 225 grams of beef are called for to
make 6 servings. If Mrs. Alferez wants to use the
recipe for 8 servings, how many grams of beef must she use?
Let N - be the number of grams required
225 : 6 = N : 8
6N = 8(225)
6N = 1800
N = 1800 / 6
N = 300 grams. * Ans.
Let N - be the number of grams required
225 : 6 = N : 8
6N = 8(225)
6N = 1800
N = 1800 / 6
N = 300 grams. * Ans.
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