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If x is even integer, which of the following must be an odd [#permalink]
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Updated on: 25 Jul 2012, 08:03
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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. \(\frac{3x^2}{2} + 1\)
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Originally posted by Stiv on 25 Jul 2012, 07:57.
Last edited by Bunuel on 25 Jul 2012, 08:03, 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]
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25 Jul 2012, 08:05
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: ifaandbarepositiveintegerssuchthatabandabare88108.htmlHope it helps.
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Re: If x is even integer, which of the following must be an odd [#permalink]
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25 Jul 2012, 21:26
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]
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29 Nov 2012, 15:04
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]
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29 Nov 2012, 15:09
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]
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29 Nov 2012, 16:06
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]
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30 Nov 2012, 03:54
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]
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30 Nov 2012, 07:40
thank you for the help.



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Re: If x is even integer, which of the following must be an odd [#permalink]
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13 Apr 2017, 01:57
Option Ex is an Even inetegr. Odd: O, Even: E & Fraction: F A. \(\frac{3x}{2}\) = \(\frac{3*E}{2}\) = \(3*E\) \(or\) \(3*O\)= \(E\) \(or\) \(O\) B. \(\frac{3x}{2}+1\) = \(\frac{3*E}{2} + 1\) = \(3*E + 1\) \(or\) \(3*O + 1\)= \(O\) \(or\) \(E\) C. \(3x^2\) = \(3E^2\) = \(3*E\) = \(E\) D. \(\frac{3x^2}{2}\) = \(\frac{3E^2}{2}\) = \(3*E\) = \(E\) E. \(\frac{3x^2}{2}+1\) = \(\frac{3E^2}{2}+1\) = \(3*E + 1\) = \(E + 1\) = \(O\)
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Re: If x is even integer, which of the following must be an odd [#permalink]
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08 Sep 2017, 22:20
if I take x=2, first option A  would be 3*2/2 = 6/2 =3 and 3 is odd..why is this wrong?



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Re: If x is even integer, which of the following must be an odd [#permalink]
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08 Sep 2017, 22:27




Re: If x is even integer, which of the following must be an odd
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08 Sep 2017, 22:27






