Problem Solving

If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x - y?
A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

Answer: C
Difficulty level: 550 - 600
Source: www.gmatprepnow.com

Brent@GMATPrepNow wrote:If 52x + 604 = 1400 and 151 + 13y = 350, what is the value of x - y?
A) -11/13
B) -11/52
C) 0
D) 11/52
E) 11/13

Answer: C
Difficulty level: 550 - 600
Source: www.gmatprepnow.com

The key here is to avoid solving the two equations for x and y.

We can do this by recognizing that each term in the equation 52x + 604 = 1400 is 4 times each term in the equation 151 + 13y = 350
For example, (4)(151) = 604
And (4)(13) = 52
And (4)(350) = 1400

So, if we take 151 + 13y = 350 and multiply both sides by 4, we get the EQUIVALENT EQUATION: 604 + 52y = 1400
Rearrange to get: 52y + 604 = 1400

So, we have:
52x + 604 = 1400
52y + 604 = 1400

Since both equations are set equal to 1400, we can say: 52x + 604 = 52y + 604
Subtract 604 from both sides to get: 52x = 52y
Divide both sides by 52 to get: x = y
If x = y, then x - y = 0

Answer: C

Cheers,
Brent