MathRevolution wrote:
Is 8^x > 4^y?
1) x > y
2) 3x > 2y
Target question: Is 8^x > 4^y?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-data-sufficiency?id=1100Notice that we can rewrite 8 and 4 with the same BASE to get:
Is (2³)^x > (2²)^y?Now apply the power of a power law to get:
Is 2^3x > 2^2y?Since 2^2y is always positive, we can safely divide both sides by 2^2y to get:
Is (2^3x)/(2^2y) > 1?Simplify to get:
Is 2^(3x - 2y) > 1?For 2^(3x -2y) to be greater than 1, the exponent, 3x - 2y, must be greater than 0.
So, we get:
REPHRASED target question: Is 3x - 2y > 0?At this point, the question can be handled quickly
Statement 1: x > y Can we use this information to answer the
REPHRASED target question?
No.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1. In this case 3x - 2y = 3(2) - 2(1) = 4. In other words,
3x - 2y > 0Case b: x = -3 and y = -4. In this case 3x - 2y = 3(-3) - 2(-4) = -1. In other words,
3x - 2y < 0Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3x > 2ySubtract 2y from both sides to get 3x - 2y > 0
PERFECT!!
This means we can answer the
REPHRASED target question with certainty. So, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent