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OG 13 - problem 41

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri May 16, 2014 1:53 pm
gdshamain wrote:41. Is 4^x+y = 8^10?

(1) x-y = 9
(2) y/x = 1/4
When posting questions, please use brackets and spaces to avoid ambiguity.
Based on your solution, the question SHOULD read:

Does 4^(x+y) = 8^10?
1) x - y =9
2) y/x = 1/4

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by Brent@GMATPrepNow » Fri May 16, 2014 1:54 pm
Does 4^(x+y) = 8^10?
1) x - y = 9
2) y/x = 1/4
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Target question: Does 4^(x+y) = 8^10?
Take 4^(x+y) = 8^10 and rewrite each side with the same base of 2 to get:
(2^2)^(x+y) = (2^3)^10
Simplify to get: 2^(2x + 2y) = 2^30 [power of a power rule]
For this equation to hold true, it must be the case that 2x + 2y = 30
Divide both sides by 2 to get x + y = 15

We can now REPHRASE our target question...
REPHRASED target question: Does x + y = 15?

Statement 1: x - y = 9
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 12 and y = 3, in which case x + y = 15
Case b: x = 10 and y = 1, in which case x + y ≠ 15
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y/x = 1/4
Cross multiply to get: x = 4y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 12 and y = 3, in which case x + y = 15
Case b: x = 8 and y = 2, in which case x + y ≠ 15
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x - y = 9
Statement 2 tells us that x = 4y
We now have a system of TWO linear equations with TWO variables, so we COULD easily solve this system for x and y, which means we COULD determine whether x + y = 15.
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

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by GMATGuruNY » Sat May 17, 2014 2:38 am
gdshamain wrote:41. Is 4^(x+y) = 8^10?

(1) x-y = 9
(2) y/x = 1/4
To answer the question stem, we need to know the value of x+y.
Question stem, rephrased: What is the value of x+y?

Statement 1: x-y=9
If x=9 and y=0, then x+y = 9+0 = 9.
If x=10 and y=1, then x+y = 10+1 = 11.
Since x+y can be different values, INSUFFICIENT.

Statement 2: y/x = 1/4
Cross-mulitplying, we get:
4y = x.
If y=1 and x=4, then x+y = 4+1 = 5.
If y=2 and x=8, then x+y = 8+2 = 10.
Since x+y can be different values, INSUFFICIENT.

Statements combined:
Since we have 2 variables and 2 distinct linear equations, we can solve for each variable.
Thus, the value of x+y can be determined.
SUFFICIENT.

The correct answer is C.
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