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

Paul4gmat · Accepted Answer

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

Sent from my A0001 using  GMAT Club Forum mobile app

sarphant · 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.

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

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards