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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Sep 06, 2014 3:15 am
If a·b≠0, and (x+a)(x+b)=0, is x=a?

(1) x−b=0

(2) a=−b
Given (x+a)(x+b)=0, either x+a = 0 or x+b = 0.

Statement 1: x-b = 0.
Thus, x+b ≠ 0, implying that x+a = 0 and that x = -a.
Thus, we know that x≠a.
SUFFICIENT.

Statement 2: a=−b.
Subtituting b=-a into (x+a)(x+b)=0, we get:
(x+a)(x-a) = 0.
If x+a = 0, then x = -a.
If x-a = 0, then x=a.
INSUFFICIENT.

The correct answer is A.
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by Matt@VeritasPrep » Sat Sep 06, 2014 10:56 am
Since ab ≠ 0, we know that a ≠ 0 and b ≠ 0. Hence a ≠ -a and b ≠ -b, as these are only true for a = 0 or b = 0.

Since (x+a) * (x+b) = 0, we know that x = -a or x = -b.

S1 tells us x = b. Since b ≠ -b, we know that x ≠ - b. Since x is either -a or -b, and x = ≠ -b, we must have x = -a. a ≠ -a, so x ≠ a. Sufficient!

S2 tells us that a = -b. So if x = -b, we know that x = a. But x could be either -a or -b (we don't know which), and -a ≠ -b, so this is insufficient: if x = -b, then x = a, but if x = -a, then x ≠ a.
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by [email protected] » Sat Sep 06, 2014 4:33 pm
Hi vivekvijayan,

This question can be solved with a combination of TESTing Values and Number Properties:

We're told that neither A nor B can equal 0. We're also told that (X+A)(X+B) = 0. We're asked if X = A. This is a YES/NO question.

Before going to the 2 Facts, let's talk about the Number Properties in this prompt:

1) A and B cannot be 0 (so they're either positive or negative values)
2) (X+A)(X+B) = 0, so at least one of the parentheses MUST = 0. Either (X+A) OR (X+B) or BOTH = 0.

Fact 1: X-B = 0

This means that X = B.
Since B cannot = 0, X cannot = 0.
Thus, (X+B) CANNOT = 0

Using the initial Number Properties, we now know that (X+A) MUST = 0.
If X = 1, A = -1, then the answer to the question is NO.
If X = -2, A = 2, then the answer to the question is NO.
If X = 5.5, A = -5.5, then the answer to the question is NO.

X and A have to be "opposites", so they will never equal one another and the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: A = -B

If A = -1, B = 1

We would then have (X - 1)(X + 1) = 0, which has two salutations (1 and -1)
If X = 1, then X does NOT equal A and the answer to the question is NO.
If X = -1, then X DOES equal A and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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