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.

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:

I know that this is easiest (and safest) by plugging in numbers, but I'm curious to know if there are any other number theory rules I could use, besides these standard rules:

O*E = E E*E = E O*O = O

Or maybe I'm just thinking too hard into the question

I know that this is easiest (and safest) by plugging in numbers, but I'm curious to know if there are any other number theory rules I could use, besides these standard rules:

O*E = E E*E = E O*O = O

Or maybe I'm just thinking too hard into the question

Well,
E+O = O
O+O = E
etc.

For this question, answer should be E.

3x^2/2 + 1

if x is even, x^2 is always even. If x is an even integer then x^2/2 is always even. E*O = E, which means 3*x^2/2 is always even. E+O = O which means 3x^2/2 + 1 is odd.

Ok, I understand that we can eliminate A, C, and D, but how can you distinguish between B & E, if the same ODD/EVEN properties apply to both?

B) 3x/2 + 1 [O*E]/[E] + O E*E + O E+O = O

E) 3x^2/2 + 1 [O*E]/[E] + O E*E + O E+O = O

I agree that the answer is E, but I see why B is confusing. I concluded in E simply b/c of process of elimination. I can disprove (b) by plugging in x=2 ==>4==>even.

I know that this is easiest (and safest) by plugging in numbers, but I'm curious to know if there are any other number theory rules I could use, besides these standard rules:

O*E = E E*E = E O*O = O

Or maybe I'm just thinking too hard into the question

Well, E+O = O O+O = E etc.

For this question, answer should be E.

3x^2/2 + 1

if x is even, x^2 is always even. If x is an even integer then x^2/2 is always even. E*O = E, which means 3*x^2/2 is always even. E+O = O which means 3x^2/2 + 1 is odd.

Ok, then, is it safe to suppose then, that every EVEN number raised to a power, divided by that same base (2), must be EVEN:

Re: If x is an even integer, which of the following must be...? [#permalink]
29 May 2010, 16:58

1

This post received KUDOS

The reason why (3X^2/2) + 1 is even is consider just X^2/2 part.

1) First X^2/2 can be written as X.X/2 2) X is even. 3) X/2 can be Even or Odd 3) That means X.X/2 is Even*Even OR Odd number 4) This number is always Even. 5) 3*Even number is Even. 6) Even number + 1 is ODD.

It is tricky. You'd only notice it without trying answers if you happened to notice that that x/2 is even for all even values except x=2 or x =-2

This is not true.

x = 6 for instance.

The easiest approach to this answer is to count the "minimum" even prime factors (aka 2s).

If we know X is even, we have at least one 2 as a factor of X.

If we have X^2, we double all those factors.

Thus, X^2/2 is guaranteed to be even.

Even + 1 = Odd

+1 for the precise explanation

In option B, given that x is 6 (2 x 3=6) for example, the 2 can be cancelled out so that 3x/2 results in 9, which is an odd integer. 9+1=10, which is even. However, once there are more than one 2s, the fraction will always result in an even number and finally add up to an odd number. _________________

Re: This is from a GMATPrep Exam: If x is an even integer, [#permalink]
26 Jan 2012, 05:27

Expert's post

1

This post was BOOKMARKED

slsu wrote:

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

A. 3x/2 B. 3x/2+1 C. 3x^2 D. 3x^2/2 E. 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 an even integer, which of the following must be an [#permalink]
19 Dec 2013, 23:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...

I got invited to interview at Sloan! The date is October 31st. So, with my Kellogg interview scheduled for this Wednesday morning, and my MIT Sloan interview scheduled...

Not all good communicators are leaders, but all leaders are good communicators. Communication is an essential tool that leaders need to use in order to get anything done. Almost...

Despite being a long weekend with Thanksgiving, this week was very tiring for me in various ways. Besides the pressure of learning materials I am not familiar with such...