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# If a and b are positive integers, which of the following

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Senior Manager
Joined: 21 Oct 2013
Posts: 408
If a and b are positive integers, which of the following  [#permalink]

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30 Jun 2014, 14:36
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Difficulty:

35% (medium)

Question Stats:

69% (01:38) correct 31% (01:43) wrong based on 240 sessions

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If a and b are positive integers, which of the following cannot be an integer?

A. (2b)/(4a+1)
B. (2b)/(3a+1)
C. (2a+1)/(4b)
D. (2a+1)/(4b+1)
E. (2a·b)/(4b+2)
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Joined: 02 Sep 2009
Posts: 60574
Re: If a and b are positive integers, which of the following  [#permalink]

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30 Jun 2014, 14:45
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goodyear2013 wrote:
If a and b are positive integers, which of the following cannot be an integer?

A) (2b)/(4a+1)
B) (2b)/(3a+1)
C) (2a+1)/(4b)
D) (2a+1)/(4b+1)
E) (2a·b)/(4b+2)

I'd first look for an option which gives odd/even for any values of a and b, because odd/even is not an integer.

Option C fits: $$\frac{2a+1}{4b}=\frac{even+odd}{even}=\frac{odd}{even}\neq{integer}$$.

To discard other A consider a=5 and b=1.
To discard other B consider a=2 and b=1.
To discard other D consider a=2 and b=1.
To discard other E consider a=3 and b=1.
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Location: India
Concentration: General Management, Technology
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Re: If a and b are positive integers, which of the following  [#permalink]

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02 Jul 2014, 03:00
$$Answer = C = \frac{2a+1}{4b}$$

Adding 1 to a multiple of 2 would always make the resultant an odd number; which is not divisible by 4
Manager
Joined: 07 Dec 2009
Posts: 84
GMAT Date: 12-03-2014
Re: If a and b are positive integers, which of the following  [#permalink]

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29 Nov 2014, 07:40
Can any one explain why not option A ?
(2b)/(4a+1)

If b = 1 and a = 5 ===> 2/21
Senior Manager
Joined: 13 Jun 2013
Posts: 253
Re: If a and b are positive integers, which of the following  [#permalink]

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29 Nov 2014, 08:53
bhatiavai wrote:
Can any one explain why not option A ?
(2b)/(4a+1)

If b = 1 and a = 5 ===> 2/21

hi, please reverse the values, put a=1 and b=5

10/5 = 2
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Posts: 13993
Re: If a and b are positive integers, which of the following  [#permalink]

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05 Sep 2018, 21:08
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Re: If a and b are positive integers, which of the following   [#permalink] 05 Sep 2018, 21:08
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