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If a and b are positive integers such that a – b and a/b are

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If a and b are positive integers such that a – b and a/b are  [#permalink]

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New post 09 Sep 2018, 09:48
adkikani wrote:
Hi niks18 chetan2u KarishmaB pikolo2510 workout gmatbusters

Could I do something with taking few additional variables?

e.g. a-b = 2 m and a/b = 2n
where m and n are integers. How do I proceed next?


Yes, I did so:

a/b = 2n , a=2bn, then

D (a+2)/2 , (2bn+2)/2 = bn+1 - because b - even, then bn - even, and bn+1 - will be always odd.
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Re: If a and b are positive integers such that a – b and a/b are  [#permalink]

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New post 16 Mar 2019, 23:40
zaarathelab wrote:
If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a + 2)/2
E. (b+2)/2


The video solution is explained here.

Answer: Option D


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Re: If a and b are positive integers such that a – b and a/b are  [#permalink]

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New post 17 Mar 2019, 07:11
zaarathelab wrote:
If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a + 2)/2
E. (b+2)/2


a-b = can both be even or odd integers
a/b ; again a & b can both be even integers or else a can be even integer multiple of 4 and b an odd integer

so out of given options
IMO D ; is correct where a a multiple of 4 will give an odd integer
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Re: If a and b are positive integers such that a – b and a/b are   [#permalink] 17 Mar 2019, 07:11

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