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

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Senior Manager
Joined: 08 Nov 2010
Posts: 404

Kudos [?]: 125 [0], given: 161

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

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27 Apr 2011, 22:58
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Difficulty:

95% (hard)

Question Stats:

36% (01:37) correct 64% (01:58) wrong based on 90 sessions

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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

_________________

Kudos [?]: 125 [0], given: 161

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Joined: 27 Apr 2011
Posts: 36

Kudos [?]: 18 [0], given: 7

Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 660 Q47 V33
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GPA: 3.37
WE: Programming (Computer Software)
Re: |a|>|b| what am i missing? [#permalink]

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27 Apr 2011, 23:11
are you sure that the answer is E? Even i think that it is C

Kudos [?]: 18 [0], given: 7

Senior Manager
Joined: 08 Nov 2010
Posts: 404

Kudos [?]: 125 [0], given: 161

Re: |a|>|b| what am i missing? [#permalink]

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27 Apr 2011, 23:58
well, i saw it in Manhattan gamt forum. and it was agreed that the answer is E. but no explanation.
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Kudos [?]: 125 [0], given: 161

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Joined: 08 May 2009
Posts: 1295

Kudos [?]: 274 [1], given: 10

Re: |a|>|b| what am i missing? [#permalink]

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28 Apr 2011, 01:17
1
KUDOS
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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Kudos [?]: 274 [1], given: 10

Senior Manager
Joined: 08 Nov 2010
Posts: 404

Kudos [?]: 125 [0], given: 161

Re: |a|>|b| what am i missing? [#permalink]

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28 Apr 2011, 01:29
so its just a typo... thanks.
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Kudos [?]: 125 [0], given: 161

Manager
Joined: 09 Aug 2010
Posts: 106

Kudos [?]: 54 [0], given: 7

Re: |a|>|b| what am i missing? [#permalink]

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28 Apr 2011, 06:21
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

Kudos [?]: 54 [0], given: 7

Senior Manager
Joined: 27 May 2012
Posts: 387

Kudos [?]: 84 [1], given: 477

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

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23 Sep 2013, 01:58
1
KUDOS
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
_________________

- Stne

Kudos [?]: 84 [1], given: 477

Math Expert
Joined: 02 Sep 2009
Posts: 41688

Kudos [?]: 124486 [0], given: 12079

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

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23 Sep 2013, 02:13
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
_________________

Kudos [?]: 124486 [0], given: 12079

Re: If a and b are integers, and |a| > |b|, is a |b| < a   [#permalink] 23 Sep 2013, 02:13
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# If a and b are integers, and |a| > |b|, is a |b| < a

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