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

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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

I'm confused how to set up the formulas here. Can any experts help?

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by GMATGuruNY » Fri Mar 09, 2018 5:36 am
grandh01 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
We can PLUG IN THE ANSWERS, which represent the miles per gallon in the city.
Since the car drove 6 fewer miles per gallon in the city than on the highway, the highway rate must be 6 greater than the tested answer choice.
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.

B: 16 miles per gallon in the city, 22 miles per gallon on the highway[/b]
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.

The correct answer is B.

An alternate line of reasoning:

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 divide 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.
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by swerve » Fri Mar 09, 2018 9:52 am
Hi ardz24,

I solved this question as follow,

Let x be a tankful of gas

462/x - 336/x = 6

462 - 336 = 6x

x = 21.

So, a tankful of gas contains 21 gallons.

Then in the city miles per gallon will be

336/21 = 16. Hence option B is the correct answer.

Regards!

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by [email protected] » Fri Mar 09, 2018 12:36 pm
Hi ardz24,

This question is perfect for TESTing THE ANSWERS (we're looking for an answer that divides evenly into 336 AND - when you add 6 to it - evenly divides into 462. How long would it take you to do the necessary division to find that answer?). The "math" approach to this prompt can actually be done in a number of ways, depending on how you want to set up the algebra. Here's another way:

Since a "tankful" of gasoline is the same number of gallons of gas whether driving on the highway or driving in the city, we can use a variation of the Distance Formula to create 2 equations:

462 = H(G) where H = miles/gallon on the highway and G = # of gallons

336 = C(G) where C = miles/gallon in the city and G = # of gallons

Right now, we have 3 variables and 2 equations. The last sentence gives us one more equation to work with: "the car traveled 6 fewer miles per gallon in the city than on the highway." This translates into:

C = H - 6

So now we have a "system" of equations (3 variables and 3 unique equations means that we CAN solve for all 3 variables). We're trying to solve for C.....

462 = H(G)
336 = C(G)
C = H - 6

H = C + 6 plug this into the first equation....

462 = (C+6)(G)
462 = CG + 6G

336 = CG plug this into the prior equation....

462 = 336 + 6G
126 = 6G
21 = G

**REMINDER: This is the value of G. We want the value of C.**

Plug G=21 into 336 = CG

336 = C(21)
16 = C

Final Answer: B

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by Jeff@TargetTestPrep » Mon Mar 12, 2018 3:36 pm
ardz24 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
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.

Answer: B

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