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# If a and b are integers, and |a| > |b|, is a |b| < a

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Manager
Joined: 01 Aug 2008
Posts: 118

Kudos [?]: 160 [0], given: 2

If a and b are integers, and |a| > |b|, is a |b| < a [#permalink]

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02 Jun 2009, 04:48
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If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

E

Need strategy/Approach to solve Inequalities. Pls Help
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Kudos [?]: 160 [0], given: 2

Manager
Joined: 08 Feb 2009
Posts: 145

Kudos [?]: 60 [0], given: 3

Schools: Anderson
Re: problem using absolute values [#permalink]

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02 Jun 2009, 05:27
(1)
If a = -2, b = -1, then the given inequality would be (-2). (1) < (-2+1). TRUE.
If a = -2, b = 0, then the given inequality would be (-2). (0) < (-2-0). FALSE.

INSUFFICIENT.

(2)
0 $$\leq$$ ab

If a = 2, b = 1, then the given inequality would be (2). (1) < (2-1). FALSE.
If a = -2, b = -1, then the given inequality would be (-2). (1) < (-2+1). TRUE.

INSUFFICIENT.

Combining,
a < 0 &&& 0 $$\leq$$ ab $$\Rightarrow$$ b $$\leq$$ 0

If a = -2, b = -1, then the given inequality would be (-2). (1) < (-2+1). TRUE.
If a = -2, b = 0, then the given inequality would be (-2). (0) < (-2-0). FALSE.

INSUFFICIENT.

Kudos [?]: 60 [0], given: 3

Senior Manager
Joined: 15 Jan 2008
Posts: 280

Kudos [?]: 49 [0], given: 3

Re: problem using absolute values [#permalink]

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04 Jun 2009, 00:43
One more for E..

when the value of b is 0, the equation doesnt hold true..

if the second statement hadnt had the equality, the answer may have been B.

Kudos [?]: 49 [0], given: 3

Re: problem using absolute values   [#permalink] 04 Jun 2009, 00:43
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# If a and b are integers, and |a| > |b|, is a |b| < a

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