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

(1) x/y = 1
(2) xy = 1

OA C

Source: GMAT Prep

We have x > 0 and y > 0. We have to determine whether x = 1.

Let's take each statement one by one.

(1) x/y = 1

Case 1: Say x = y = 1, the answer is Yes.
Case 2: Say x = y = 2, the answer is No.

No unique answer. Insufficient.

(2) xy = 1

Case 1: Say x = y = 1, the answe is Yes.
Case 2: Say x = 2 and y = 1/2, the answer is No.

No unique answer. Insufficient.

(1) and (2) together

From x/y = 1, we have x = y; thus, from xy =1, we have x ^2 = 1 => x = ±1; however, we know that x > 0; thus, x = 1. The answer is Yes. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:If x and y are greater than 0, is x = 1 ?

(1) x/y = 1
(2) xy = 1

OA C

Source: GMAT Prep

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 1
Case b: x = 2 and y = 2. In this case, the answer to the target question is NO, x does NOT equal 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy = 1
There 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 1
Case b: x = 2 and y = 1/2. In this case, the answer to the target question is NO, x does NOT equal 1
Since 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 = y
Now 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 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent