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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  [#permalink]

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New post 03 Jul 2018, 09:49
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

78% (01:03) correct 22% (01:23) wrong based on 186 sessions

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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following  [#permalink]

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New post 03 Jul 2018, 09:56
2
oskarw93s wrote:
B

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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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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following  [#permalink]

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New post 03 Jul 2018, 10:37
1
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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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following  [#permalink]

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New post 17 Jul 2018, 17:09
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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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following  [#permalink]

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New post 17 Jul 2018, 21:53
1
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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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following  [#permalink]

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New post 04 Aug 2019, 09:56
1
The Strategy -
Both of them have to be of same sign for the condition to be valid.
Hence B.


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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following   [#permalink] 04 Aug 2019, 09:56
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