Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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

Show Tags

29 Nov 2012, 14:09

1

This post received KUDOS

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
_________________

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?

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...