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# Is a < b ?

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Intern
Joined: 07 Jan 2013
Posts: 3
Is a < b ?  [#permalink]

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02 Aug 2013, 09:37
4
00:00

Difficulty:

75% (hard)

Question Stats:

49% (01:54) correct 51% (01:25) wrong based on 110 sessions

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Is a < b ?

(1) a < 2b
(2) 2a < b
Senior Manager
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Is a < b ?  [#permalink]

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02 Aug 2013, 09:57
2
1
gepetow wrote:
Is a < b ?

1. a < 2b
2. 2a < b

Thx

Statement 1
a < 2b
If b=2 then a<4 or "a" can be 3, 1
Thus Insufficient

Statement 1
2a < b
If b=4 then a<2 or "a" can be 1 ,0 ----> a<b in this case
but
If b=-4 then a<-2 or "a" can be -3 ,-4,-5 ----> Thus Insufficient

Statement 1 & 2
a < 2b
2a < b
3a<3b
a<b
Sufficient

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Re: Is a < b ?  [#permalink]

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02 Aug 2013, 10:00
gepetow wrote:
Is a < b ?

1. a < 2b
2. 2a < b

Thx

From F.S 1 : For a=b=1, 2b>a and a=b.We get a NO.
For a=-1,b=1,2b>a and b>a. We get a YES.Insufficient.

From F.S 2 : For a=0,b=1, b>2a and a<b.We get a YES.
For a=b=-1,b>2a and b=a. We get a NO.Insufficient.

Taking both togehter and upon adding : 3a<3b = a<b. Sufficient.

C.
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Re: Is a < b ?  [#permalink]

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08 Feb 2018, 04:11
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Re: Is a < b ? &nbs [#permalink] 08 Feb 2018, 04:11
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