Quantitative Reasoning Reviewer 11 (Problem Solving Skills)
1. Tom borrowed $600 at 10% per year, simple interest, for 3 years. How much did he have to repay (principal + interest) at the end of the 3 year period?
a. $780
b. $650
c. $680
d. $590
e. $740
Answer: A
The interest to pay is given by:
Interest = 600 * 10% * 3 = $180
Total to repay
600 + 180 = $780
2. Anne can finish a job in 10 days. Together, Rachel and Anne can finish the same job in 7 days. How many days will it take Rachel to finish the job alone?
a. 3/7
b. 20 1/3
c. 23 1/3
d. 70/3
e. 3/70
Answer: C
70x ( ⅒ + ¹/ₓ = ⅒) 70x
70x/10 + 70x/x = 70x/x
7x + 70 = 10x
70= 10x - 7x
70=3x
Answer= 23 1/3
3. Which of the following is equal to 85 percent of 160?
a. 1.88
b. 136
c. 188
d. 13,600
e. 13.6
Answer: B
85% of 160
0.85 X 1600.85 X 160 = 136
Answer is 136
4. The original price of a shirt was $20. It was decreased to $15 . What is the percent decrease of the price of the shirt?
a. 20%
b. 30%
c. 45%
d. 25%
e. 30%
Answer: D
The absolute decrease is:
20 - 15 = $5
The percent decrease is the absolute decrease divided by the original price (part/whole).
percent decease = 5 / 20 = 0.25
Multiply and divide 0.25 to obtain percent.
percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25%
5. If a Play Station 4 was bought for $558 after a 10% discount, what was the original price of the Play Station 4?
a. $660
b. $700
c. $550
d. $680
e. $620
Answer: E
Step 1:
Let the original price be = x
Discount rate = 10%
Step 2:
Discount = 10% of x = 0.10 × x = 0.1x
Sale price = Original price − Discount = x − 0.1x = 0.9x
Step 3:
Sale price = $558 = 0.9x
Solving for x
x = 558/0*9 = $620
So, original price = $620
6. Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of:
a. 20%
b. 21%
c. 23%
d. 18%
e. Cannot be determined
Answer: A
The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them are increased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%, on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer: 20%
7. If a picture frame is 27 cm long and 18 cm wide, what is the ratio of its length to its width?
a. 5:3
b. 4:2
c. 6:3
d. 3:2
e. 2:3
Answer: D
8. A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.
a. $35
b. $45
c. $70
d. $60
e. $80
Answer: A
The markup is 40% of the $25 cost, so the markup is:
(0.40)(25) = 10
Then the selling price, being the cost plus markup, is:
25 + 10 = 35
Answer= $35
9. There are only 350,000 who voted which is just 20% of the registered voters. What is the total number of registered voters?
a. 1,750,000
b. 1,750
c. 95,000
d. 17,000
e. 70,000
Answer: A
350,000/ 0.20 = 1,750,000
Related:
1. Logical Reasoning Reviewer
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a. $780
b. $650
c. $680
d. $590
e. $740
Answer: A
The interest to pay is given by:
Interest = 600 * 10% * 3 = $180
Total to repay
600 + 180 = $780
2. Anne can finish a job in 10 days. Together, Rachel and Anne can finish the same job in 7 days. How many days will it take Rachel to finish the job alone?
a. 3/7
b. 20 1/3
c. 23 1/3
d. 70/3
e. 3/70
Answer: C
70x ( ⅒ + ¹/ₓ = ⅒) 70x
70x/10 + 70x/x = 70x/x
7x + 70 = 10x
70= 10x - 7x
70=3x
Answer= 23 1/3
3. Which of the following is equal to 85 percent of 160?
a. 1.88
b. 136
c. 188
d. 13,600
e. 13.6
Answer: B
85% of 160
0.85 X 1600.85 X 160 = 136
Answer is 136
4. The original price of a shirt was $20. It was decreased to $15 . What is the percent decrease of the price of the shirt?
a. 20%
b. 30%
c. 45%
d. 25%
e. 30%
Answer: D
The absolute decrease is:
20 - 15 = $5
The percent decrease is the absolute decrease divided by the original price (part/whole).
percent decease = 5 / 20 = 0.25
Multiply and divide 0.25 to obtain percent.
percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25%
5. If a Play Station 4 was bought for $558 after a 10% discount, what was the original price of the Play Station 4?
a. $660
b. $700
c. $550
d. $680
e. $620
Answer: E
Step 1:
Let the original price be = x
Discount rate = 10%
Step 2:
Discount = 10% of x = 0.10 × x = 0.1x
Sale price = Original price − Discount = x − 0.1x = 0.9x
Step 3:
Sale price = $558 = 0.9x
Solving for x
x = 558/0*9 = $620
So, original price = $620
6. Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of:
a. 20%
b. 21%
c. 23%
d. 18%
e. Cannot be determined
Answer: A
The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them are increased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%, on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer: 20%
7. If a picture frame is 27 cm long and 18 cm wide, what is the ratio of its length to its width?
a. 5:3
b. 4:2
c. 6:3
d. 3:2
e. 2:3
Answer: D
8. A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.
a. $35
b. $45
c. $70
d. $60
e. $80
Answer: A
The markup is 40% of the $25 cost, so the markup is:
(0.40)(25) = 10
Then the selling price, being the cost plus markup, is:
25 + 10 = 35
Answer= $35
9. There are only 350,000 who voted which is just 20% of the registered voters. What is the total number of registered voters?
a. 1,750,000
b. 1,750
c. 95,000
d. 17,000
e. 70,000
Answer: A
350,000/ 0.20 = 1,750,000
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1. Logical Reasoning Reviewer
2. Reading Comprehension Reviewer