Is a=âˆ’b?

(1) aÂ·b > b^2

(2) a^2 = b^2

The OA is A.

Why is the first statement sufficient? May someone helps me? Thanks in advanced.

## Is a=âˆ’b?

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- Rich.C@EMPOWERgmat.com
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We're asked if A = (-B). This is a YES/NO question and can be solved by TESTing VALUES and/or with Number Properties. This question essentially asks if A and B are exact opposites of one another (for example 3 and -3).

1) (A)(B) > B^2

With the inequality in Fact 1, we know that B cannot equal 0.

IF....

B = Positive, then B^2 = positive and A would have to be GREATER than B for the inequality to 'work.' In this case, A and B could NEVER be opposites, so answer to the question is ALWAYS NO.

B = Negative, then B^2 = positive and A would have to be NEGATIVE. In this case, A and B could NEVER be opposites, so the answer to the question is ALWAYS NO.

Fact 1 is SUFFICIENT

(2) A^2 = B^2

IF...

A=1 and B=1, then the answer to the question is NO

A=1 and B= -1, then the answer to the question is YES

Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,

Rich

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- Brent@GMATPrepNow
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VJesus12 wrote:Is a = âˆ’b?

(1) ab > bÂ²

(2) aÂ² = bÂ²

**Target question:**

**Is a = âˆ’b?**

This is a good candidate for rephrasing the target question.

*Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100*

Take the equation a = âˆ’b and add b to both sides to get: a + b= 0

So, we get....

**REPHRASED target question:**

**Is a + b= 0?**

**Statement 1: ab > bÂ²**

When it comes to inequalities, we must be careful when we multiply or divide both sides by a variable. If that variable has a POSITIVE value, the direction of the inequality DOES NOT CHANGE. If that variable has a NEGATIVE, value the direction of the inequality REVERSES.

Since we don't know whether b is positive or negative, we must examine both cases:

Case a: b is positive. Take ab > bÂ² and divide both sides by b to get: a > b

IMPORTANT: if b is positive, then a must also be positive (since a > b).

If a and b are BOTH positive, then the sum a + b must be positive.

In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0

Case b: b is negative. Take ab > bÂ² and divide both sides by b to get: a < b (notice that we reversed the inequality symbol)

IMPORTANT: if b is negative, then a must also be negative (since a < b).

If a and b are BOTH negative, then the sum a + b must be negative.

In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0

Notice that both cases yielded the same answer to the REPHRASED target question.

Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

**Statement 2: aÂ² = bÂ²**

There are several values of a and b that satisfy statement 2. Here are two:

Case a: a = 0 and b = 0, in which case a + b = 0 + 0 = 0. In this case, the answer to the REPHRASED target question is YES, a+b DOES equal 0

Case b: a = 1 and b = 1, in which case a + b = 1 + 1 = 2. In this case, the answer to the REPHRASED target question is NO, a+b does NOT equal 0

Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

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- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**14926**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1265 members**GMAT Score:**770

VJesus12 wrote:Is a=âˆ’b?

(1) aÂ·b > b^2

(2) a^2 = b^2

The OA is A.

Why is the first statement sufficient? May someone helps me? Thanks in advanced.

**Target question:**

**What is the value of x?**

**Given: xÂ³ < xÂ²**

If we do a little bit of work, we'll see that this given information tells us A LOT about x

xÂ² must be POSITIVE here (since we can see that x â‰ 0, otherwise we can't have xÂ³ < xÂ²). So, we can safely divide both sides of the inequality by xÂ² to get: x < 1

So, x < 1 AND x â‰ 0

**Statement 1: -2< x < 2**

There are several values of x that satisfy statement 1 (and the given information). Here are two:

Case a: x = -1

Case b: x = 0.5

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

**Statement 2: x is an integer greater than -2**

So, x is an INTEGER that's less than 1, but greater than -2 AND x â‰ 0

There's only one x-value (x = -1) that satisfies these conditions. So, x must equal -1

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,

Brent

Brent Hanneson - Creator of GMATPrepNow.com

Watch these

And check out these

**If you enjoy my solutions, I think you'll like my GMAT prep course**Watch these

**video reviews**of my courseAnd check out these

**free resources**