PhillyBound wrote:

If x and y are greater than 0, is x = 1 ?

(1) x/y = 1

(2) xy = 1

Target question: Is x = 1 ? Given: x and y are POSITIVE Statement 1: x/y = 1 Let's TEST some values.

There are several values of x and y that satisfy statement 1. Here are two:

Case a: x = 1 and y = 1. In this case, the answer to the target question is

YES, x DOES equal 1Case b: x = 2 and y = 2. In this case, the answer to the target question is

NO, x does NOT equal 1Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy = 1There are several values of x and y that satisfy statement 2. Here are two:

Case a: x = 1 and y = 1. In this case, the answer to the target question is

YES, x DOES equal 1Case b: x = 2 and y = 1/2. In this case, the answer to the target question is

NO, x does NOT equal 1Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that x/y = 1

Statement 2 tells us that xy = 1

Take x/y = 1 (statement 1) and multiply both sides by y to get:

x = yNow take xy = 1 (statement 2) and replace

y with

x to get: (x)(

x) = 1

Simplify: x² = 1

This means EITHER x = 1, OR x = -1

However, since we're told that x is POSITIVE, it must be the case that

x = 1 So, the answer to the target question is

YES, x DOES equal 1Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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