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# If a and b are integers, is b/a even? (1) b/a^2 is odd. (2) a is even.

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Math Expert
Joined: 02 Sep 2009
Posts: 53738
If a and b are integers, is b/a even? (1) b/a^2 is odd. (2) a is even.  [#permalink]

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10 Jul 2018, 21:27
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Difficulty:

65% (hard)

Question Stats:

60% (02:07) correct 40% (01:49) wrong based on 71 sessions

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If a and b are integers, is b/a even?

(1) b/a^2 is odd.

(2) a is even.

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Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
If a and b are integers, is b/a even? (1) b/a^2 is odd. (2) a is even.  [#permalink]

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10 Jul 2018, 21:32
1
1
Bunuel wrote:
If a and b are integers, is b/a even?

(1) b/a^2 is odd.

(2) a is even.

Statement 1: $$\frac{b}{a^2}=Odd$$

$$=>\frac{b}{a}*\frac{1}{a}=Odd =>\frac{b}{a}=Odd*a$$

So whether $$\frac{b}{a}$$ is even or odd will depend on the value of $$a$$. if $$a$$ is even then $$\frac{b}{a}$$ is even and if $$a$$ is odd then $$\frac{b}{a}$$ is odd. Insufficient

Statement 1: Nothing mentioned about $$b$$. Insufficient

Combining 1 & 2: we know $$\frac{b}{a}=Odd*a=Odd*Even=Even$$. Sufficient

Option C
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Re: If a and b are integers, is b/a even? (1) b/a^2 is odd. (2) a is even.  [#permalink]

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19 Aug 2018, 21:36
1. if a is odd, b must be odd. b/a must be odd
if a is even, b must be even. let a=2n,b=2m; b/a^2=2m/4n^2=2k+1
b/a=m/n=2n*(2k+1) even
NS
2. 6/2=3; 8/2=4. NS
1+2:
even
Re: If a and b are integers, is b/a even? (1) b/a^2 is odd. (2) a is even.   [#permalink] 19 Aug 2018, 21:36
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