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DS- Number Prop

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DS- Number Prop

by akhilsuhag » Sun Jan 04, 2015 6:54 am
If a·b≠0, and (x+a)(x+b)=0, is x=a?
(1) x−b=0
(2) a=−b
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Source: — Data Sufficiency |

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by [email protected] » Sun Jan 04, 2015 10:58 am
Hi akhilsuhag,

This DS question is based on the idea that (anything)(0) = 0.

We're told that neither A nor B can equal 0 and that (X+A)(X+B) = 0. This means that.....
1) (X+A) = 0
2) OR (X+B) = 0
3) OR BOTH = 0.

We're asked if X=A?

This question can be answered by TESTing VALUES or by using Number Properties.

**Note: For the answer to this question to be YES, then (X+B) MUST = 0. However, for the answer to this question to be NO, either term or both could = 0**

Fact 1: X-B = 0

This means X = B. Since B cannot = 0, (X+B) is NOT = 0.
By extension, this means that (X+A) MUST = 0
So X and A are opposite values and the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT.

Fact 2: A = -B

Here, I'm going to TEST VALUES. This Fact tells us that A and B are opposite values.

IF...
A = 2
B = -2
We have....
(X+2)(X-2) = 0
If X = 2, then X=A and the answer to the question is YES
If X = -2, then X does NOT = A and the answer to the question is NO
Fact 2 is INSUFFICIENT.

Final Answer: A

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by Matt@VeritasPrep » Mon Jan 05, 2015 11:23 am
Here's a succinct approach.

Since (x + a)(x + b) = 0, we must have either (x + a) = 0, in which case x = -a, or (x + b) = 0, in which case x = -b. So we know x = -a or -b. Since a ≠ 0, we know that a ≠ -a. Hence if x = -a, x ≠ a. So the question is REALLY "Is x = -a?"

S1 tells us that x = b. Since x = b, we can't have x = -b. x must equal either -a or -b, however, so x = -a. SUFFICIENT!

S2 tells us that a = -b. So if x = -b, then x = a. But if x = -a, then x ≠ a. Since we could have either of these be true, this statement is NOT SUFFICIENT.
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