Quantitative Reasoning Reviewer 9 (Problem Solving Skills)
1. An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles; the entire trip took three hours.
Find the distance from the airport to the corporate offices.
a. 120 miles
b. 180 miles
c. 150 miles
d. 130 miles
e. 200 miles
Answer: A
Since we have been asked to find the distance from the airport to the corporate office (that is the distance he spent flying), let us assign that specific value as 'x'.
Thus, the distance he spent driving will be '150 - x'
Now, in the first row, we have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent driving in terms of 'x'.
Time(1) = Distance(1)/Speed(1) = (150 - x)/30
Similarly, in the second row, we again have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent flying in terms of 'x'.
Time(2) = Distance(2)/Speed(2) = x/60
Now, notice that we have both the times in terms of 'x'. Also, we know the total time for the trip. Thus, summing the individual times spent driving and flying and equating it to the total time, we can solve for 'x'.
Time(1) + Time(2) = Time(3) --> (150 - x)/30 + x/60 = 3 --> x = 120 miles
Answer : 120 miles
2. If a watch is losing 1.5 minutes for every 12 hours that go by, how many minutes will it lose in one week?
a. 22
b. 26
c. 23
d. 24
e. 21
Answer: E
The given ratio is 1.5 minutes / 12 hours.
equation: 1.5 minutes = x minutes 12 hours 1 week
Note: We need to convert 1 week to hours because the units must be the same.
use: 24 hours = 1 day, 7 days = 1 week,
therefore: 1 week = 168 hours (24∙ 7)
equation: 1.5 minutes = x minutes
12 hours 168 hours
solve: 1.5(168) = 12x 21 = x
The watch will lose 21 minutes in one week.
3. John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?
a. 265
b. 256
c. 233
d. 240
e. 234
Answer: C
John can build a wall in 30 days and Peter can demolish the same wall in 40 days So, in ONE day, John can build 1/30 of the entire wall And, in ONE day, Peter can demolish 1/40 of the entire wall So, AFTER TWO DAYS, the portion of the wall standing = 1/30 - 1/40 = 1/120 So, AFTER TWO DAYS, 1/120 of the wall is built (and remains standing)
So, after FOUR DAYS, 2/120 of the wall is built (and remains standing) And after SIX DAYS, 3/120 of the wall is built (and remains standing) And after 232 DAYS, 116/120 of the wall is built (and remains standing) On DAY 233, it's John's turn to build. Remember that, in ONE day, John can build 1/30 of the entire wall In other words, in ONE day, John can build 4/120 of the entire wall
So, after 232 DAYS, 116/120 of the wall was built, and on the 233rd day, John built the remaining 4/120 of the wall.
So, WALL COMPLETE!!
Answer: 233
4. An item that regularly sells for $425 is marked down to $318.75. What is the discount rate?
a. 45%
b. 25%
c. 35%
d. 30%
e. 40%
Answer: B
First, find the amount of the markdown:
425 – 318.75 = 106.25
Then calculate "the markdown over the original price", or the markdown rate: ($106.25) is (some percent) of ($425), so:
106.25 = (x)(425)
...and the relative markdown over the original price is:
x = 106.25 ÷ 425 = 0.25
Answer= 25%
5. Sarah is making bead necklaces as treats for her party. She has 90 green beads and 108 blue beads. What is the greatest number of identical necklaces she can make if she wants to use all of the beads?
a. 16
b. 11
c. 12
d. 15
e. 18
Answer: E
6. Our school has 8 male teachers who comprise 25% of all our teachers. How many teachers do we have?
a. 42
b. 62
c. 52
d. 32
e. 22
Answer: D
7. At a toy factory it takes two machines 50 minutes to create 10 teddy bears. How many teddy bears can one machine create in 30 minutes?
a. 2
b. 6
c. 3
d. 7
e. 5
Answer: C
First, find how many teddy bears one machine can create in 50 minutes:
10 ÷ 2 = 5
Now find how long it takes one machine to create 1 teddy bear:
50 ÷ 5 = 10 minutes per teddy bear At last find how many teddy bears the machine can create in 30 minutes:
30 ÷ 10 = 3 teddy bears
8. While covering a distance or 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in m/s?
a. 1.33
b. 1.55
c. 1.21
d. 1.66
e. 1.12
Answer: D
Let us take the distance traveled till now as d
So, d= 5/7 * (24-d)
which gives d=10 km = 10000 m
1 hr 40 min = 100*60 seconds
s=d/t = 10000/100*60 = 1.66
9. Teejay bought an ice cream from Japanese convenience store with a tagged price of ¥5,000. The cashier told them that the ice cream is subject to 5% tax. How much Teejay has to pay?
a. ¥4,750
b. ¥3,250
c. ¥250
d. ¥5,500
e. ¥5,250
Answer: E
5,000 x 0.05 = 250
5,000 + 250 = 5,250
Answer = ¥5,250
10. A coat was sold at a 30% discount sale for $140. What was the original price of the coat?
a. $350
b. $200
c. $400
d. $230
Answer: B
$1 Let x = the original price of the coat
A coat was sold at a 30% discount sale for $140
Another way to state this is to say that, during the sale, people paid 70% of the original price
That is: 70% of x = $140
Or: 0.7x = 140
Solve to get: x = 140/0.7 = 200
Answer: $200
Related:
1. Logical Reasoning Reviewer
2. Criminal Justice System Reviewer
3. Quantitative Reasoning Reviewer 10
Find the distance from the airport to the corporate offices.
a. 120 miles
b. 180 miles
c. 150 miles
d. 130 miles
e. 200 miles
Answer: A
Since we have been asked to find the distance from the airport to the corporate office (that is the distance he spent flying), let us assign that specific value as 'x'.
Thus, the distance he spent driving will be '150 - x'
Now, in the first row, we have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent driving in terms of 'x'.
Time(1) = Distance(1)/Speed(1) = (150 - x)/30
Similarly, in the second row, we again have the distance in terms of 'x' and we have been given the speed. Thus we can calculate the time he spent flying in terms of 'x'.
Time(2) = Distance(2)/Speed(2) = x/60
Now, notice that we have both the times in terms of 'x'. Also, we know the total time for the trip. Thus, summing the individual times spent driving and flying and equating it to the total time, we can solve for 'x'.
Time(1) + Time(2) = Time(3) --> (150 - x)/30 + x/60 = 3 --> x = 120 miles
Answer : 120 miles
2. If a watch is losing 1.5 minutes for every 12 hours that go by, how many minutes will it lose in one week?
a. 22
b. 26
c. 23
d. 24
e. 21
Answer: E
The given ratio is 1.5 minutes / 12 hours.
equation: 1.5 minutes = x minutes 12 hours 1 week
Note: We need to convert 1 week to hours because the units must be the same.
use: 24 hours = 1 day, 7 days = 1 week,
therefore: 1 week = 168 hours (24∙ 7)
equation: 1.5 minutes = x minutes
12 hours 168 hours
solve: 1.5(168) = 12x 21 = x
The watch will lose 21 minutes in one week.
3. John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?
a. 265
b. 256
c. 233
d. 240
e. 234
Answer: C
John can build a wall in 30 days and Peter can demolish the same wall in 40 days So, in ONE day, John can build 1/30 of the entire wall And, in ONE day, Peter can demolish 1/40 of the entire wall So, AFTER TWO DAYS, the portion of the wall standing = 1/30 - 1/40 = 1/120 So, AFTER TWO DAYS, 1/120 of the wall is built (and remains standing)
So, after FOUR DAYS, 2/120 of the wall is built (and remains standing) And after SIX DAYS, 3/120 of the wall is built (and remains standing) And after 232 DAYS, 116/120 of the wall is built (and remains standing) On DAY 233, it's John's turn to build. Remember that, in ONE day, John can build 1/30 of the entire wall In other words, in ONE day, John can build 4/120 of the entire wall
So, after 232 DAYS, 116/120 of the wall was built, and on the 233rd day, John built the remaining 4/120 of the wall.
So, WALL COMPLETE!!
Answer: 233
4. An item that regularly sells for $425 is marked down to $318.75. What is the discount rate?
a. 45%
b. 25%
c. 35%
d. 30%
e. 40%
Answer: B
First, find the amount of the markdown:
425 – 318.75 = 106.25
Then calculate "the markdown over the original price", or the markdown rate: ($106.25) is (some percent) of ($425), so:
106.25 = (x)(425)
...and the relative markdown over the original price is:
x = 106.25 ÷ 425 = 0.25
Answer= 25%
5. Sarah is making bead necklaces as treats for her party. She has 90 green beads and 108 blue beads. What is the greatest number of identical necklaces she can make if she wants to use all of the beads?
a. 16
b. 11
c. 12
d. 15
e. 18
Answer: E
6. Our school has 8 male teachers who comprise 25% of all our teachers. How many teachers do we have?
a. 42
b. 62
c. 52
d. 32
e. 22
Answer: D
7. At a toy factory it takes two machines 50 minutes to create 10 teddy bears. How many teddy bears can one machine create in 30 minutes?
a. 2
b. 6
c. 3
d. 7
e. 5
Answer: C
First, find how many teddy bears one machine can create in 50 minutes:
10 ÷ 2 = 5
Now find how long it takes one machine to create 1 teddy bear:
50 ÷ 5 = 10 minutes per teddy bear At last find how many teddy bears the machine can create in 30 minutes:
30 ÷ 10 = 3 teddy bears
8. While covering a distance or 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in m/s?
a. 1.33
b. 1.55
c. 1.21
d. 1.66
e. 1.12
Answer: D
Let us take the distance traveled till now as d
So, d= 5/7 * (24-d)
which gives d=10 km = 10000 m
1 hr 40 min = 100*60 seconds
s=d/t = 10000/100*60 = 1.66
9. Teejay bought an ice cream from Japanese convenience store with a tagged price of ¥5,000. The cashier told them that the ice cream is subject to 5% tax. How much Teejay has to pay?
a. ¥4,750
b. ¥3,250
c. ¥250
d. ¥5,500
e. ¥5,250
Answer: E
5,000 x 0.05 = 250
5,000 + 250 = 5,250
Answer = ¥5,250
10. A coat was sold at a 30% discount sale for $140. What was the original price of the coat?
a. $350
b. $200
c. $400
d. $230
Answer: B
$1 Let x = the original price of the coat
A coat was sold at a 30% discount sale for $140
Another way to state this is to say that, during the sale, people paid 70% of the original price
That is: 70% of x = $140
Or: 0.7x = 140
Solve to get: x = 140/0.7 = 200
Answer: $200
Related:
1. Logical Reasoning Reviewer
2. Criminal Justice System Reviewer
3. Quantitative Reasoning Reviewer 10