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A car traveled 462 miles per tankful of gasoline on the...

by swerve » Sun Dec 31, 2017 6:21 am

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A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by EconomistGMATTutor » Sun Dec 31, 2017 11:32 am
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Hi swerve,
Let's take a look at your question.

On Highway, using a tank full of gasoline a car traveled = 462 miles
In city, using a tank full of gasoline a car traveled = 336 miles

Let, On Highway, miles per gallon the car traveled = x miles, then
In city, miles per gallon the car traveled = (x-6) miles

We will be using ratios to solve this problem,
$$\frac{462}{336}=\frac{x}{x-6}$$
$$\frac{231}{168}=\frac{x}{x-6}$$
$$231\left(x-6\right)=168x$$
$$231x-1386=168x$$
$$231x-168x=1386$$
$$63x=1386$$
$$x=\frac{1386}{63}$$
$$x=22$$

We need to find, how many miles per gallon did the car travel in the city?
In city, miles per gallon the car traveled = (x-6) miles
In city, miles per gallon the car traveled = 22-6 = 16 miles

Option B is correct.

Hope it helps.
I am available if you'd like any follow up.
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462 miles

by GMATGuruNY » Mon Jan 01, 2018 9:31 am
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
An alternate approach is to PLUG IN THE ANSWERS, which represent the miles per gallon in the city.
When the correct answer choice is plugged in, the same amount of gas -- in other words, ONE TANKFUL -- will be required to travel 336 miles in the city and 462 miles on the highway.

Since all of the values in the problem are INTEGERS, the correct answer choice must divide evenly into the distance traveled in the city (336).
336 = 2*3*7*8.
Eliminate D (2*11) and E (3*3*3), neither of which divides evenly into 2*3*7*8.

Since on the highway 6 more miles per gallon are traveled, 6 more than the correct answer choice must divide evenly into the distance traveled on the highway (462).
Adding 6 to each of the remaining answer choices, we get:
A: 14+6 = 20 = 2*2*5.
B: 16+6 = 22 = 2*11.
C: 21+6 = 27 = 3*3*3.
Since 462 = 2*3*7*11, only B (2*11) divides evenly into the distance traveled on the highway.

The correct answer is B.

Answer choice B: 16 miles per gallon in the city, 22 miles per gallon on the highway
At a rate of 16 miles per gallon, the amount of gas required to travel 336 miles in the city = 336/16 = 21 gallons.
At a rate of 22 miles per gallon, the amount of gas required to travel 462 miles on the highway = 462/22 = 21 gallons.
Success!
The same amount of gas -- 21 gallons -- is sufficient to travel 336 miles in the city and 462 miles on the highway.
Last edited by GMATGuruNY on Tue Aug 18, 2020 9:40 am, edited 1 time in total.
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by Scott@TargetTestPrep » Sat Aug 24, 2019 4:22 am
swerve wrote:A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

We can create the proportion in which x = miles per gallon on the highway and (x - 6) = miles per gallon in the city.

(x - 6)/336 = x/462

462x - 2,772 = 336x

126x = 2,772

x = 22

So city mpg = 22 - 6 = 16 mpg.

Alternate Solution:

Let the capacity of the car be n gallons. Then, the car's gas mileage is 462/n miles per gallon on the highway and 336/n miles per gallon in the city. Since we are given that the difference is 6, we have:

462/n - 336/n = 6

126 = 6n

n = 21

Since the capacity of the car is 21 gallons, the care made 336/21 = 16 miles per gallon in the city.

Answer: B

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by Brent@GMATPrepNow » Sat Aug 24, 2019 5:50 am
swerve wrote:A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

(A) 14
(B) 16
(C) 21
(D) 22
(E) 27

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
The car burns a tankful of gas on the highway and a tankful of gas in the city.

So, we can start with this WORD EQUATION: (volume of gas used on the highway) = (volume of gas used in the city)

Key formula: gallons of gas used = (distance traveled)/(rate of miles traveled per gallon)
So, the word equation becomes: (distance traveled on highway)/(highway fuel consumption rate) = (distance traveled in city)/(city fuel consumption rate))

Let x = the rate of fuel consumption in the city (in miles per gallon)
So x+6 = the rate of fuel consumption on highway (in miles per gallon)
The car traveled 462 miles on the highway and 336 miles in the city.

Plug the values into the equation to get to get: 462/x+6 = 336/x
Cross multiply to get: 462x = 336(x + 6)
Expand to get: 462x = 336x + 2016
Subtract 336x from both sides to get: 126x = 2016
Solve: x = 2016/126 = 16

Answer: B

Cheers,
Brent
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by rishab0507 » Tue Aug 27, 2019 8:33 am
its an question of averages , and can be solved by using putting values from answers, But will be lengthy process.
As both in city and highway give same average, we can make a simple equation
Let it travelled : x
462/x = 336/ x-6
336x = 462x- 2772
126x = 2772
x= 22, which is av given on highway
In City , 22-6= 16
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