A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any

Question

A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.
2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank

(1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.

(2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank

hellosanthosh2k2 · Accepted Answer

Let there be x gallons of fuel X, and y gallons of fuel Y

question: cost per gallon? = (3x + 5y)/(x + y)
 all we need is relation between x and y, or the ratio of x and y

Statement 1: Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles
pretty straight forward, x + y = 8, 20x + 40y = 200, two equations to find x and y => suff

Statement 2: The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank
 Total miles can cover / total cost = 50/7
 (20x + 40y)/(3x + 5y) = 50/7 => rearranging we get, 3y = x, so we found the relation between x and y => sufficient

(D)

GMAT TIGER · Answer

D.

1) 20x + 40 (8-x) = 200. 
x = Fuel x and y = 8-x
x = 6
y = 2. suff.

2) 20/3 (a) + 40/5 (1-a) = 50/7

a = 9/14
1-a = 5/14

fraction of $ for fuel x + fraction of $ for fuel y = 1
a = fraction of $ for fuel x 
1-a = fraction of $ for fuel y

suff...

wcgc · Answer

I'm sorry but I don't get the 2nd equation. Can you explain why 20/3(a) = fraction of $ for fuel x?

unplugged · Answer

Great explanation GMATTIGER!

@wcgmatclub - 
For every dollar spent on Fuel X, you can travel 20/3 miles
For every dollar spent on Fuel Y, you can travel 40/5 miles

For every dollar spent on the mixture of X and Y, you can travel 7 1/7 miles. The question is asking what is the mixture?

Therefore, a(20/ 3) + (1-a)40/5 = 50/7

Cheers,
Unplugged

AKY13 · Answer

Hi GMAT-mate,

To further the solution to find what is needed, won't the equation be as below for statement 2- 
9/14 * 3 + 5/14 * 5 = 26/7

For statement 1, the answer is 
(6*3+2*5)/8 = 28/8

The 2 figures aren't matching. In GMAT-DS, the solution has to be consistent for each statements if the answer is D.

Have I done some mistake.

Rebaz · Answer

What does a and (1-a) stand for? I donot get this part.

Thanks in advance!

bumpbot · Answer

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A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any

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