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If a and b are integers, and |a| > |b|, is a |b| < a [#permalink ]
27 Apr 2011, 21:58

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71% (01:52) wrong

based on 69 sessions
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

|a|>|b| when a=-2, b = -1 a*|b|<a-b? so, -2*1<-2+1? -2<-1 - YES. when a=-2, b=1 -2*1<-2-1? -2<-3? NO. so statement 1 is Ins. st. 2: a*b=0 so B is zero (A cannot be = 0 bc his distance from zero is bigger than b's distance |a|>|b|) so:a*|b|<a-b? 0<a we disregard stm.1 so a can be <>0 means - no answer here as well. if we put both of them in: i dont c why u cannot tell if 0<a when a<0. it will always be smaller than 0 what am i missing?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-integers-and-a-b-is-a-b-a-83804.html
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Re: |a|>|b| what am i missing? [#permalink ]
27 Apr 2011, 22:11

are you sure that the answer is E? Even i think that it is C

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Re: |a|>|b| what am i missing? [#permalink ]
27 Apr 2011, 22:58

well, i saw it in Manhattan gamt forum. and it was agreed that the answer is E. but no explanation.

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Re: |a|>|b| what am i missing? [#permalink ]
28 Apr 2011, 00:17
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144144 wrote:

If a and b are integers, and |a| > |b|, is a · |b| < a – b? (1) a < 0 (2) ab >= 0 |a|>|b| when a=-2, b = -1 a*|b|<a-b? so, -2*1<-2+1? -2<-1 - YES. when a=-2, b=1 -2*1<-2-1? -2<-3? NO. so statement 1 is Ins. st. 2: a*b=0 so B is zero (A cannot be = 0 bc his distance from zero is bigger than b's distance |a|>|b|) so:a*|b|<a-b? 0<a we disregard stm.1 so a can be <>0 means - no answer here as well. if we put both of them in: i dont c why u cannot tell if 0<a when a<0. it will always be smaller than 0 what am i missing?

combining 1 and 2

a is negative

b can be 0 or negative.

Hence, by plugging in some numbers OA will be E.

Refer to Ron's discussion here -

http://www.manhattangmat.com/forums/if- ... t9437.html _________________

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Re: |a|>|b| what am i missing? [#permalink ]
28 Apr 2011, 00:29

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Re: |a|>|b| what am i missing? [#permalink ]
28 Apr 2011, 05:21

Given that |a| > |b|, this means a has a bigger digit than b, regardless of signIs a |b| > a - b? (1) a <0 Let a=-3 and b=-2 -5(-2) > -3 - (-2)? 6 > -1 Yes! Let a=-3 and b=2 -5(2) > -3 - (2)? -6 > -5 No! INSUFFICIENT!(2) ab >= 0 Since we know |a| > |b|[\m\ then a cannot be 0 but b can OR a and b both negative [m]Let a=-3 and b=0 -3(0) > -3 - 0? 0 > -3 No! Let a=-3 and b=-2 -3(-2) > -3 + 2? 6 > -1 Yes! INSUFFICIENT!Therefore E

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Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink ]
23 Sep 2013, 00:58
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144144 wrote:

If a and b are integers, and |a| > |b|, is a · |b| < a – b? (1) a < 0 (2) ab = 0

Question should be corrected as second statement is

ab \geq 0 not just ab = 0

based in the present form OA should be C

This will prevent confusion

Thank you

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Re: If a and b are integers, and |a| > |b|, is a |b| < a [#permalink ]
23 Sep 2013, 01:13

Re: If a and b are integers, and |a| > |b|, is a |b| < a
[#permalink ]
23 Sep 2013, 01:13

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