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

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Senior Manager
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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:

35% (02:26) correct 65% (01:59) wrong based on 86 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

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Kudos [?]: 17 [0], given: 7

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
Senior Manager
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Posts: 409
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Kudos [?]: 116 [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 [?]: 254 [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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Senior Manager
Joined: 08 Nov 2010
Posts: 409
Followers: 8

Kudos [?]: 116 [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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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
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Kudos [?]: 74 [1] , given: 449

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
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- Stne

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Kudos [?]: 105925 [0], given: 11593

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