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ps 500 test22 #20

by dunkin77 » Sun Apr 15, 2007 10:33 am
Hi,

The correct answer to this is B) but again, :( could not figure out. can anyone please help?

20. 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
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by jayhawk2001 » Sun Apr 15, 2007 12:47 pm
Let me be the number of miles per gallon on the highway.

For a tankful of gasoline,

462 / m = 336 / (m-6)
Solving m = 22

Hence miles in the city = 22-6 = 16
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by ns88 » Sun Apr 15, 2007 2:26 pm
Dunkin,

I enjoy the math problems you are posting up. It’s a good way to practice.

In some cases, to save time, I’m trying to solve the questions backwards.


I see that you give away the answer in the first line. Could you please post the answer in the last line after the problem? Or you don’t even have to post the answer, which is even better. I’m sure some math wiz will come up with it.


Thanks.

NS88
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by Cybermusings » Mon Apr 16, 2007 5:09 am
Car traveled 426 - 336 = 126 miles per tankful of gasoline less in the city compared to the highway.
Car traveled 6 fewer miles per gallon in the city than on the highway
Therefore the tank capacity of the car = 126/6 = 21 gallons
In 21 gallons the car travels 462 miles on the highway or 22 miles/gallon
In 21 gallons the car travels 336 miles in the city or 16 miles/gallon
Hence the answer should be B
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by BTGmoderatorRO » Sun Dec 24, 2017 5:26 am
LEt the total number of gallons in a full tank be k. This implies that
The car covers 462 miles on the highway with k, gallons and it covers 336miles in the city with k gallons. Let x, y be the number of miles covered per gallon by the car on the highway and city respectively.

x miles/gallon * K gallons =462
y miles/gallon * K gallons = 336

xK =462......eqn 1
yK =336......eqn 2

Dividing eqn 1 by 2
$$\frac{X}{Y}$$ = $$\frac{462}{336}$$ = $$\frac{11}{8}$$ ....eqn 3
From the question , X=Y+6
Putting this eqn into 3
$$\frac{Y+6}{Y}$$ = $$\frac{11}{8}$$
8Y+48=11Y
11Y-8Y=48
Y= $$\frac{48}{3}$$ =16
The nnumber of cars covered by the car in the city per gallon is 16.
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by GMATWisdom » Sun Dec 24, 2017 10:37 am
dunkin77 wrote:Hi,

The correct answer to this is B) but again, :( could not figure out. can anyone please help?

20. 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
IF Y GALLONS IS THE CAPACITY OF THE TANK THEN AS PER THE STATEMENT THE CAR IS DRIVEN AT 462/Y MILES PER GALLONS ON THE HIGHWAY AND 336/Y MILES PER GALLON IN THE CITY AND THE DIFFERENCE BETWEEN THEM IS 6 MILES PER GALLON
THEREFORE 462/Y -336/Y = 6
OR 126/Y = 6 OR Y = 126/6=21 GALLONS
HENCE IN THE CITY THE CAR TRAVELS 336/21= 16 MILES PER GALLON
OPTION B IS CORRECT.
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