Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Feb 2012
Posts: 142
Concentration: Finance, Economics

If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
Updated on: 25 Jul 2012, 07:03
Question Stats:
74% (01:15) correct 26% (00:57) wrong based on 311 sessions
HideShow timer Statistics
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. \(\frac{3x^2}{2} + 1\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Stiv on 25 Jul 2012, 06:57.
Last edited by Bunuel on 25 Jul 2012, 07:03, edited 1 time in total.
Edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 61385

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
25 Jul 2012, 07:05
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.
_________________



Senior Manager
Joined: 28 Mar 2012
Posts: 293
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
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.
Regards,



Intern
Joined: 29 Nov 2012
Posts: 6

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
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.



Board of Directors
Joined: 01 Sep 2010
Posts: 3379

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
29 Nov 2012, 14:09
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
_________________



Intern
Joined: 29 Nov 2012
Posts: 6

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
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?



Math Expert
Joined: 02 Sep 2009
Posts: 61385

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
30 Nov 2012, 02:54
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.
_________________



Intern
Joined: 29 Nov 2012
Posts: 6

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
30 Nov 2012, 06:40
thank you for the help.



Manager
Joined: 18 Oct 2016
Posts: 128
Location: India
WE: Engineering (Energy and Utilities)

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
13 Apr 2017, 00:57
Option E
x 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. \(\frac{3x^2}{2}+1\) = \(\frac{3E^2}{2}+1\) = \(3*E + 1\) = \(E + 1\) = \(O\)



Manager
Joined: 30 Apr 2013
Posts: 73

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
08 Sep 2017, 21:20
if I take x=2, first option A  would be 3*2/2 = 6/2 =3 and 3 is odd..why is this wrong?



Math Expert
Joined: 02 Sep 2009
Posts: 61385

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
08 Sep 2017, 21:27
santro789 wrote: if I take x=2, first option A  would be 3*2/2 = 6/2 =3 and 3 is odd..why is this wrong? The question asks which of the following MUST be odd, not COULD be odd. Option A could be odd but it's not always odd while E is odd for any even x. Hope it's clear.
_________________



Senior Manager
Joined: 12 Sep 2017
Posts: 313

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
01 Jan 2019, 19:51
.Hello experts!
I answered correctly this one but after that, I started to think the next doubt:
If 0 is considered an even number...
Then D is not going to become an integer because 0*2 will be 1 so:
(3(1) divided by 2) + 1
What am I doing wrong?
Thank you so much!



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4841
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x is even integer, which of the following must be an odd
[#permalink]
Show Tags
17 Jan 2020, 10:11
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. \(\frac{3x^2}{2} + 1\) Plug in and try to negate  A. \(\frac{3x}{2}\) Or, \(\frac{3*4}{2} = 6\) B. \(\frac{3x}{2} + 1\) Or,\(\frac{3*6}{2} + 1 = 10\) C. \(3x^2\) Or, \(3*2^2 = 12\) D. \(\frac{3x^2}{2}\) Or, \(\frac{3*2^2}{2} = 6\) (E) Plug in any number it will always be ODD, Answer must be (E)
_________________




Re: If x is even integer, which of the following must be an odd
[#permalink]
17 Jan 2020, 10:11






