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If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |

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Math Expert
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If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |  [#permalink]

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New post 01 Nov 2018, 00:19
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Difficulty:

  35% (medium)

Question Stats:

71% (01:33) correct 29% (01:34) wrong based on 142 sessions

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Re: If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |  [#permalink]

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New post 01 Nov 2018, 01:41
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Bunuel wrote:
If abc ≠ 0, is a (b + c) ≥ 0?

(1) |b + c| = |b| + |c|
(2) |a + b| = |a| + |b|


Question: is a (b + c) ≥ 0?

To answer this question we need
1) Sign of a (without knowing the absolute value of a)
2) Sign of (b+c)

Statement 1: |b + c| = |b| + |c|

i.e. b and c both have same sign
i.e. either ba nd c both are positive or both are negative
Sign of a is unknown also sign of (b+c) is unknown hence
NOT SUFFICIENT

Statement 2: |a + b| = |a| + |b|

i.e. b and a both have same sign
i.e. either b and a both are positive or both are negative
Sign of a is unknown also sign of (b+c) is unknown hence
NOT SUFFICIENT

Combining the two statements

Case 1: all a, b and c are positive, in this case a (b + c) is Greater than 0
Case 2: all a, b and c are Negative, in this case also a (b + c) is Greater than 0 hence
SUFFICIENT

Answer: Option C
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Re: If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |  [#permalink]

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New post 21 Nov 2018, 13:27
Bunuel wrote:
If abc ≠ 0, is a (b + c) ≥ 0?

(1) |b + c| = |b| + |c|
(2) |a + b| = |a| + |b|



Hi Bunuel,

any simpler approach to solve the question.
Please help!!!
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If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |  [#permalink]

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New post 21 Nov 2018, 18:15
Case 2: all a, b and c are Negative, in this case also a (b + c) is Greater than 0 hence

how is a, b and c negative but addiction of b + c (two negative numbers) is greater than zero... that's less than zero since answer is a negative number.


did not even see the a(b+c) as the a had space between (b+c) and I assumed it was just a typo.
never mind then.
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If abc ≠ 0, is a (b + c) ≥ 0? (1) |b + c| = |b| + |c| (2) |a + b| = |   [#permalink] 21 Nov 2018, 18:15
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