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

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If a and b are integers, and |a| > |b|, is a |b| < a [#permalink] New post 27 Apr 2011, 21:58
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:34) correct 69% (01:52) wrong based on 71 sessions
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

[Reveal] Spoiler:
|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
[Reveal] Spoiler: OA

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Re: |a|>|b| what am i missing? [#permalink] New post 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] New post 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] New post 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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Senior Manager
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Re: |a|>|b| what am i missing? [#permalink] New post 28 Apr 2011, 00:29
so its just a typo... thanks.
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Re: |a|>|b| what am i missing? [#permalink] New post 28 Apr 2011, 05:21
Given that |a| > |b|, this means a has a bigger digit than b, regardless of sign

\(Is a |b| > a - b?\)
\((1) a <0\)

\(Let a=-3 and b=-2\)
\(-5(-2) > -3 - (-2)?\)
\(6 > -1 Yes!\)

\(Let a=-3 and b=2\)
\(-5(2) > -3 - (2)?\)
\(-6 > -5 No!\)

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] New post 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] New post 23 Sep 2013, 01:13
Expert's post
stne wrote:
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


The answer would still be E.

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