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Is |a - b| < |a| + |b| ? (1) a/b < 0 (2) a^2*b < 0

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Director
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Joined: 02 Oct 2017
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Is |a - b| < |a| + |b| ? (1) a/b < 0 (2) a^2*b < 0  [#permalink]

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New post 27 Jul 2018, 06:59
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Difficulty:

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Question Stats:

45% (02:11) correct 55% (01:54) wrong based on 49 sessions

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Is |a - b| < |a| + |b| ?

(1) a/b < 0

(2) a^2*b < 0
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Joined: 02 Aug 2009
Posts: 6540
Re: Is |a - b| < |a| + |b| ? (1) a/b < 0 (2) a^2*b < 0  [#permalink]

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New post 27 Jul 2018, 08:09
]Is |a-b|<|a|+|b|

This will happen when both X and y are of different signs...
In |a-b|, both a and B will get added if they are different signs and it's Modulus will be equal to |a|+|b|

1)a/b <0
This means both a and B are of opposite sign..
Sufficient

2)a^2*b<0
b<0, but we cannot say if a is negative or positive as a^2 will always be positive
Insufficient

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is |a - b| < |a| + |b| ? (1) a/b < 0 (2) a^2*b < 0  [#permalink]

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New post 27 Jul 2018, 10:50
We need to check if a and b have same signs, only then the given statement holds true.

(1) a/b = -ve, therefore a and b have opposite signs. Sufficient.

(2) a^2*b<0, therefore b is negative. But no information about a as square of any number is always positive. Insufficient.

Hence, A.
Re: Is |a - b| < |a| + |b| ? (1) a/b < 0 (2) a^2*b < 0 &nbs [#permalink] 27 Jul 2018, 10:50
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