Assume the car traveled x mpg on the highway and (x - 6) mpg in city. It then follows that:
462/x = 336/(x - 6) since both mileages (462 and 332) are on a tankful of gasoline.
336x = 462x - 2772 => -126x = -2772 => x = 22
So in the city, the car travels 22 - 6 = 16 mpg.
Choose B.
miles
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truplayer256
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We can PLUG IN THE ANSWERS, which represent the miles per gallon in the city.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
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 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.
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 Wed Sep 17, 2014 9:57 am, edited 1 time in total.
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336/x=y, 336=xy; 462/x=y+6, 462=xy+6x where x-number of galons and y-number of miles per galon
combining both equztions we get 462=336+6x, so x=21, number of miles per galon in the city is 336/21=16, so answer is B
Hope that helps!
combining both equztions we get 462=336+6x, so x=21, number of miles per galon in the city is 336/21=16, so answer is B
Hope that helps!
