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Is a=−b?

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Is a=−b?

by VJesus12 » Fri Apr 06, 2018 2:33 am
Is a=−b?

(1) a·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.

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by Rich.C@EMPOWERgmat.com » Fri Apr 06, 2018 4:24 pm
Hi VJesus12,

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
Contact Rich at Rich.C@empowergmat.com
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by Brent@GMATPrepNow » Sun Apr 08, 2018 6:35 am
VJesus12 wrote:Is a = −b?

(1) ab > b²

(2) a² = b²
Target question: Is a = −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 = −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 > b²
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 > b² 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 > b² 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: a² = b²
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
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by Brent@GMATPrepNow » Tue Sep 17, 2019 7:59 am
VJesus12 wrote:Is a=−b?

(1) a·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: x³ < x²
If we do a little bit of work, we'll see that this given information tells us A LOT about x
x² must be POSITIVE here (since we can see that x ≠ 0, otherwise we can't have x³ < x²). So, we can safely divide both sides of the inequality by x² to get: x < 1
So, x < 1 AND x ≠ 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 ≠ 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
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