If |a| + |b| = |a + b|, a 0, and b 0, then which of the following

Question

If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true? A. ab < 0 B. ab > 0 C. a - b > 0 D. a + b < 0 E. a + b > 0

sarphant · Accepted Answer

The Strategy -
Both of them have to be of same sign for the condition to be valid.
Hence B.

Please press kudos, if I was able to help you. Thank you.

Paul4gmat · Answer

For this equation to be true .. a and b both should either positive or negative .. Which is ab>0 .. Hence B.

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gmatexam439 · Answer

Hi, just stating the answer won't help anyone including yourself. Try to elaborate on the approach you used to solve the question; that way, if you would have had any wrong in your strategy then someone might be able to point that out, helping the community !

KSBGC · Answer

Given

|a| + |b| = |a + b|

Let assume the value of a and b

a = -2 or 2

b = -2 or 2

Both cases given equation is true. Either both of the a and b are positive or both of them are negative. Other combinations are not working here.

Thus ab>0 is true.

The best answer is B.

chetan2u · Answer

|When is this possible, ONLY when both a and b are on same side of 0 or in other words both have same sign...
Please see attached figure..

If a and b are of same sign a*b>0

B

adityateewari · Answer

|a+b| > 0
(a+b)^2 > 0

a^2 + b^2 + 2ab > 0

first two components will be > 0. Therefore ab has to be greater than 0

CEdward · Answer

If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?

The stem impies that a and b share the same sign. Either both are positive or both are negative.

A. ab < 0

B. ab > 0 Correct. Irrespective of whether they are both positive or negative, this will always be true.

C. a - b > 0

D. a + b < 0

E. a + b > 0

Answer is B.

playthegame · Answer

I squared both sides to get |a| X |b| = a x b this means that a and b have the same sign. I did not know before hand that if |a| + |b| = |a+b| then a and b have the same sign so had to do this extra step, I will remember now.

Thanks,

bumpbot · Answer

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If |a| + |b| = |a + b|, a 0, and b 0, then which of the following

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If |a| + |b| = |a + b|, a 0, and b 0, then which of the following

Prep Toolkit

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