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

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Bunuel
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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   03 Jul 2018, 09:49
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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
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B
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Paul4gmat
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   03 Jul 2018, 10:37
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Bunuel wrote:
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
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
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   03 Jul 2018, 09:56
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oskarw93s wrote:
B

Posted from my mobile device


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 !
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chetan2u
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   17 Jul 2018, 21:53
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Bunuel wrote:
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


|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
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PicsArt_07-18-10.22.49.jpg
PicsArt_07-18-10.22.49.jpg [ 51.16 KiB | Viewed 7224 times ]

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sarphant
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   04 Aug 2019, 09:56
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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.
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   17 Jul 2018, 17:09
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Bunuel wrote:
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



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.
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B
adityateewari
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   27 Aug 2019, 03:43
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|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
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CEdward
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following [#permalink] New post   25 Jan 2021, 23:44
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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.
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playthegame
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Re: If |a| + |b| = |a + b|, a 0, and b 0, then which of the following [#permalink] New post   08 Feb 2024, 09:54
Bunuel wrote:
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

­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,
 
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Re: If |a| + |b| = |a + b|, a 0, and b 0, then which of the following [#permalink]
08 Feb 2024, 09:54
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