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
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
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