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If x is even integer, which of the following must be an odd

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If x is even integer, which of the following must be an odd [#permalink] New post 25 Jul 2012, 06:57
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If x is even integer, which of the following must be an odd integer?

A. \frac{3x}{2}
B. \frac{3x}{2} + 1
C. 3x^2
D. \frac{3x^2}{2}
E. \frac{3x^2}{2} + 1
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Jul 2012, 07:03, edited 1 time in total.
Edited the question.
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 29 Nov 2012, 14:09
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buymovieposters wrote:
I narrowed this question down to B and E. Based on the rules alone why couldn't it be B?

(3x/2)+1

if x is even then we have an even + odd which would be odd?

thanks for the clarification.


Because the theory is important but also to reach the answer through the most efficient way.

x=2(as statement says) OR x=4 (thanks this we know for instance that A is not always true)

\frac{6}{2}= 3+ 1 = 4 OR 7 (is not always true: one time even one time odd). That's it Same for the other answer choices. You can obtain E in 30 seconds
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 30 Nov 2012, 02:54
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buymovieposters wrote:
I narrowed this question down to B and E. Based on the rules alone why couldn't it be B?

(3x/2)+1

if x is even then we have an even + odd which would be odd?

thanks for the clarification.


That's not correct.

Given that x is even, thus x=2k for some integer k. Substitute in option B:

\frac{3x}{2}+1=\frac{3*2k}{2}+1=3k+1 --> if k=odd then 3k+1=odd+1=even but if k=even then 3k+1=even+1=odd.

As you can see \frac{3x}{2}+1 can be even (for example if x is 2, 6, 10, ...) as well as odd (for example if x is 4, 8, 12, ...).

Hope it's clear.
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 25 Jul 2012, 07:05
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Stiv wrote:
If x is even integer, which of the following must be an odd integer?

A. \frac{3x}{2}
B. \frac{3x}{2} + 1
C. 3x^2
D. \frac{3x^2}{2}
E. \frac{3x^2}{2} + 1



One can spot right away that if x is any even number then x^2 is a multiple of 4, which makes \frac{x^2}{2} an even number and therefore \frac{3x^2}{2}+1=3*even+1=even+1=odd.

Answer: E.

If you don't notice this, then one also do in another way. Let x=2k, for some integer k, then:

A. \frac{3x}{2}=\frac{3*2k}{2}=3k --> if k=odd then 3k=odd but if k=even then 3k=even. Discard;

B. \frac{3x}{2}+1=\frac{3*2k}{2}+1=3k+1 --> if k=odd then 3k+1=odd+1=even but if k=even then 3k+1=even+1=odd. Discard;

C. 3x^2 --> easiest one as x=even then 3x^2=even, so this option is never odd. Discard;

D. \frac{3x^2}{2}=\frac{3*4k^2}{2}=6k^2=even, so this option is never odd. Discard;

E. \frac{3x^2}{2}+1=\frac{3*4k^2}{2}=6k^2+1=even+1=odd, thus this option is always odd.

Answer: E.

Similar question to practice: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html

Hope it helps.
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 25 Jul 2012, 20:26
Hi,

Since, x is even we can assume x = 2 or x = 4,
such that x/2 is both odd/even as per the value of x.

Check each option with these values. We get the answer when both x=2, 4 gives an odd value.

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Re: If x is even integer, which of the following must be an odd [#permalink] New post 29 Nov 2012, 14:04
I narrowed this question down to B and E. Based on the rules alone why couldn't it be B?

(3x/2)+1

if x is even then we have an even + odd which would be odd?

thanks for the clarification.
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 29 Nov 2012, 15:06
thanks.

certainly i'm trying to answer "odd/even" questions in the most efficient manner possible.

what i would have done on the real CAT is narrowed it down to B and E, then like you let x = 2 or 4 and plugged in to see.

i kind of got tripped up. typically when we multiply a integer by an even we ALWAYS get an even but (3/2) is frac, therefore multiplying it by an even may or may not make it even?
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Re: If x is even integer, which of the following must be an odd [#permalink] New post 30 Nov 2012, 06:40
thank you for the help.
Re: If x is even integer, which of the following must be an odd   [#permalink] 30 Nov 2012, 06:40
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