BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:23 pm

Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

Answer: C
Source: Official Guide

So, we have to determine whether (x^2 – y^2) = (x + y)(x – y) is a positive number.

Let's take each statement one by one.

(1) x – y is a positive number.

Case 1: Say x = 2 and y = 1.

(x^2 – y^2) = (x + y)(x – y) = (2 + 1)(2 – 1) = 3, a positive number. The answer is yes.

Case 2: Say x = 2.1 and y = 1.1.

(x^2 – y^2) = (x + y)(x – y) = (2.1 + 1.1)(2.1 – 1.1) = 3.2*1 = 3.2, not a positive number. The answer is no. Insufficient.

(2) x + y is a positive number.

On the same basis as discussed in Statement 1, Statement 2 is insufficient.

(1) and (2) together

So, we have (x^2 – y^2) = (x + y)(x – y) = A positive Integer*A positive Integer = A positive Integer

The correct answer: C

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:23 pm

Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

Answer: C
Source: Official Guide

The key to answering this question is the first recognize that x² – y² = (x + y)(x - y)
This allows us to rephrase our target question as follows:

Target question: Is (x + y)(x - y) a positive number?

Statement 1: x – y is a positive number
Here we know that (x - y) is positive, but we know nothing about (x + y)
To see what I mean, consider these two possible cases that satisfy statement 1:

Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is YES, (x + y)(x - y) IS a positive number
Case b: x = 1 and y = -2. In this case, (x + y)(x - y) = (1 + (-2))(1 - (-2)) = -3. So, the answer to the target question is NO, (x + y)(x - y) is NOT a positive number
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y is a positive number.
Here we know that (x + y) is positive, but we know nothing about (x - y)
Consider these two possible cases that satisfy statement 2:

Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is YES, x² – y² IS a positive number
Case b: x = -1 and y = 2. In this case, (x + y)(x - y) = ((-1) + 2)((-1) - 2) = -3. So, the answer to the target question is NO, x² – y² is NOT a positive number
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) is POSITIVE
Statement 2 tells us that (x + y) is POSITIVE
So, (x + y)(x - y) = (POSITIVE)(POSITIVE) = POSITIVE
The answer to the target question is YES, x² – y² IS a positive number
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent