A car traveled 462 miles per tankful of gasoline on the highway and 33

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

Answer is B

Hope its clear
Cheers
J

Let the speed in highway be h mpg and in city be c mpg.
h = c+6

h miles are covered in 1 gallon
462 miles will be covered in 462/h.

Similarly c miles are covered in 1 gallon
336 miles will be covered in 336/c.

Both should be same (as car's fuel capacity does not change with speed)
=> 336/c = 462/h
=> 336/c = 462/(c+6)
=> 336c+336*6=462c
=>c=336*6/126=16

Answer B.

mpg(c) = 336/m

mpg(h) = 462/m

336/m=462/m - (6)

solve for m to get m=21. plug back into 336/21 to get 16

Similar question to practice: a-certain-car-averages-25-miles-per-gallon-of-gasoline-when-128139.html

Solution without making complex Algebraic equations

462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city.

i.e. Difference of Miles per tankful of gasoline = 462 - 336 = 126 miles

Given : 6 fewer miles per gallon in the city than on the highway

i.e. Difference of 6 miles comes in one gallon when car travels on Highway and in City
so Difference of 126 miles will come in = 126/6 = 21 gallons

i.e. Car travels 336 miles in 21 gallons in City

i.e. Mileage of car in City = 336/21 = 16 Miles per gallon

Answer: Option

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?


let x=city mpg
336/462=8/11
8/11=x/(x+6)
x=16 mpg
B

Hi All,

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:

GMAT assassins aren't born, they're made,
Rich

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

Dear Brent,
I want to understand the logic. How come the miles are different in the highway than in the city?

Can you help please?
Thanks

Due to all of the stops and starts (due to traffic lights, crosswalks, etc) a car's fuel consumption is typically lower in the city that its fuel consumption on the highway.
So, the car can travel further on the highway (on 1 tank of gas) than it can travel in the city (on 1 tank of gas)

Does that help?

Cheers,
Brent

Given total distance = 462, 336
n = number of mpg
g = number of gallons

Highway --> 462 = (n+6)(g)
City --> 336 = (n)(g)

336/g = n

462 = (336/g + 6)(g)
462 = 336 + 6g
126 = 6g
g = 21

336/21 = n
16 = n

We can 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.

.

Answer choice [spoiler]B[/spoiler]: 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.

Let x be full tank per gallon.

Miles per gallon in the highway = 462x

Miles per gallon in the city = 336x

6 fewer miles per gallon in the city than on the highway:

462x - 6 = 336x

x = 1/21 full tank per gallon

Miles per gallon in the city:

336(1/21) = 16 miles per gallon.

Answer is B.

It is a simple question on DIRECT VARIATION.

If miles/tankful will increase, miles/gallon will also increase.

Therefore, ratios of the two factors should be constant.
Let 'X' be the rate in miles per gallon for the CITY. So, for the HIGHWAY it will be (X + 6) miles per gallon

462/(X+6) = 336/X
=> X = 16

Answer is B

let total gallons of fuel in car be x
we know
462/x - 336/x = 6
126 = 6x
x= 21
mileage in city ; 336/21 ; 16
option B

IMO B
In Highway, N gallons gives x miles = 462
N * X = 462

In City, N gallons gives x-6 miles = 336
N * (X-6) = 336 ---------------------------(a)
NX - 6N = 336
462 - 6N = 336
N = 21 gallons

Substitute in city eqn (a)
X-6 = 336/N = 336/21 = 16 gallons per mile in city

Question: 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?
(You will find this question in the Official Advanced Document too.)

A question like this can immediately put you on the track of framing algebraic equations and using variables to get to a solution.
However I would refrain from that here and see if we can think logically and arrive at an answer !
#1 The logical route

GMAT Track of Thought 1

Highways are usually free of traffic checks and hence there is less of fuel consumed when travelling on a highway which implies a larger distance covered on highways instead of the city roads for the same volume of fuel.
Thus, this car too covers 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city.
What is the additional distance it travels??
Its 462 - 336 =126 additional miles per unit volume of fuel or 126 additional miles per gallon.
The car also travels 6 lesser miles in traffic roads as compared to highways

GMAT Track of Thought 2

So this car travelled additional 126 miles on highway as its mileage was +6 miles per gallon on highway.
Hence the fuel consumption in gallon = \(\frac{Additional Distance}{ Additional distance covered per gallon}\)
= \(\frac{121 }{ 6}\)
= 21 gallons

GMAT Track of Thought 3
Distance covered by the car being 336 miles in the city, the miles per gallon that the car travel in the city, considering the volume of fuel in th etank is constant for city and highway= 336 / 21
= 16 miles/ gallon
(option b)

#2 The Algebraic Approach

Alternately, you can go the algebraic route of framing equations and solving through.
Let 'g' be the number of gallons in one tankful of fuel.
Then the number of "miles per gallon" on the highways is 462/g which is 6 more than 336/g (number of "miles per gallon" in the city)

=> \(\frac{462}{g}\) = 6+ \(\frac{336}{g}\\
\)
=> \(\frac{126}{g}\) = 6

=> g = 21 gallons

Thus number of "miles per gallon" in the city = \(\frac{336 }{21}\\
\)
=16 miles
(option b)

PS: You have been assigned a mountain so that you can show how its moved! Keep moving through the obstacles till you get to the score you aimed for.


Devmitra Sen
GMAT Mentor