# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

If x^2 = y^2, is true that x>0?

I. x=2y+1

II. y<= -1

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

### Difficulty Level

Hard### Solution

Option C is the correct answer.

### Option Analysis

x^2=y^2 –> |x|=|y| –> either y=x or y=−x.

Statement I is insufficient: x=2y+1 –> if y=x then we would have: x=2x+1 –> x=−1<0 (notice that in this case y=x=−1) but if y=−x then we would have: x=−2x+1 –> x=1/3>0 (notice that in this case y=−x=−1/3). Not sufficient.

Statement II is insufficient: y<= -1. Clearly insufficient.

Together I and II, Since from (2) y≤−1 then from (1) y=x=−1, so the answer to the question is NO. Sufficient.

### Related Questions

- Color X ink is created by blending red, blue, green and yellow inks in the ratio 6:5:2:2. What is the number…

- Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home…

- What is the value of expression x(x-2)^3 when x = -1?

- On May 1 of last year, Jasmin invested x dollars in a new account at an interest rate of 6 percent per…

- What is the circumference of circular region R?