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:

Re: Even and Odd : GMATPrep [#permalink]
17 Dec 2009, 04:32

zaarathelab wrote:

If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer? A. a/2 B. b/2 C. (a+b)/2 D. (a + 2)/2 E. (b+2)/2

is the question correct?? none of the options seem to satisfy

here a>b since a/b is even integer

let a= 24 and b = 4.

A. a/2 = 12 => even B. b/2 = 2 => even C. (a+b)/2 = 14 => even D. (a+2)/2 = 13 => odd E. (b+2)/2 = 3 =>odd

now if a = 20 and b = 2 then a-b = 18 and a/b = 10 A. a/2 = 10 => even B. b/2 = 1 => odd C. (a+b)/2 = 11 => odd D. (a+2)/2 = 13 => odd E. (b+2)/2 = 2 => even

Re: Even and Odd : GMATPrep [#permalink]
17 Dec 2009, 04:38

14

This post received KUDOS

Expert's post

6

This post was BOOKMARKED

zaarathelab wrote:

If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer? A. a/2 B. b/2 C. (a+b)/2 D. (a + 2)/2 E. (b+2)/2

\(a-b\) even --> either both even or both odd

\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.

As both statements are true --> \(a\) and \(b\) must be even.

As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.

Options A is always even. Options B can be even or odd. Options C can be even or odd. Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd. Options E can be even, odd.

Re: Even and Odd : GMATPrep [#permalink]
17 Dec 2009, 04:41

1

This post was BOOKMARKED

kp1811 wrote:

zaarathelab wrote:

If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer? A. a/2 B. b/2 C. (a+b)/2 D. (a + 2)/2 E. (b+2)/2

is the question correct?? none of the options seem to satisfy

here a>b since a/b is even integer

let a= 24 and b = 4.

A. a/2 = 12 => even B. b/2 = 2 => even C. (a+b)/2 = 14 => even D. (a+2)/2 = 13 => odd E. (b+2)/2 = 3 =>odd

now if a = 20 and b = 2 then a-b = 18 and a/b = 10 A. a/2 = 10 => even B. b/2 = 1 => odd C. (a+b)/2 = 11 => odd D. (a+2)/2 = 13 => odd E. (b+2)/2 = 2 => even

what the heck.... ...D it will be...sorry for oversight from my end

Re: Even and Odd : GMATPrep [#permalink]
17 Dec 2009, 08:35

3

This post received KUDOS

Expert's post

sagarsabnis wrote:

I didnt get why a has to be multiple of 4

Now if u take a as 4 and b as 2 then a-b is even a/b is even and a+b/2 is odd which is option C.

Please explain where i am going wrong?

First question: Why \(a\) has to be multiple of 4?

As we concluded \(a\) and \(b\) have to be even integers to meet both conditions in the stem: \(a=2m\) and \(b=2n\).

Then we have \(\frac{a}{b}\) is an even integer: \(\frac{a}{b}=2k\) --> \(a=2bk=4kn\) --> \(a\) is a multiple of \(4\).

Second question: Option C also COULD give an even result, so why not C?

The question asks: "which of the following MUST be an odd integer?"

If we take \(a=16\) and \(b=4\), then \(\frac{a+b}{2}=10=even\). So option C may or may not be odd and we are asked to determine which option is ALWAYS odd, hence C is out.

In fact: Options A is always even. Options B can be even or odd. Options C can be even or odd. Options D is always odd. Options E can be even or odd.

Re: If a and b are positive integers [#permalink]
26 Oct 2010, 07:45

1

This post received KUDOS

Given: a > 0, b > 0 and a, b are Integers

a - b and a/b are both even intergers ==> \(a - b = 2m_1\) \(\frac{a}{b} = 2m_2\) ==> \(a = (b)(2m_2)\) ==> a & b are both even, otherwise the above conditions won't be satisfied.

Now lets go with options one by one ... A) a/2 ==> can be even or odd ( a = 6 or a = 8)

B) b/2 ==> Can be either even or odd ( b = 6 or b = 8)

C) (a+b) /2 ==> Since, \(a = (b)(2m_2)\), \(\frac{a + b}{2}\) =\(\frac {(b)(2m_2) + b}{2}\) ==> \(\frac{a + b}{2}\) =\(\frac {(b)(2m_2 + 1)}{2}\) ==> Can be even or odd

D) (a+2)/2 ==> \(\frac{a + b}{2}\) =\(\frac{2bm_2 + 2}{2}\) ==> \(\frac{a + b}{2}\) =\(bm_2 + 1\) ==> Since, b is even, \(bm_2\) is even and \(bm_2 + 1\) is odd always

E) (b+2)/2 ==> \(\frac{b+2}{2} = 1 + \frac{b}{2}\) ==> Can be even or odd _________________

Cheers! Ravi

If you like my post, consider giving me some KUDOS !!!

a and b both have to be even to fulfill the condition. a could be = 4, 6, 8 ...., b = 2,4, .... so a - b = 2 (Even) a/b= 2k (Even) a/2=2k a = 4k so a must be multiple of 4 now try the options ans. D _________________

Re: Even and Odd : GMATPrep [#permalink]
21 May 2012, 05:13

kp1811 wrote:

zaarathelab wrote:

If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer? A. a/2 B. b/2 C. (a+b)/2 D. (a + 2)/2 E. (b+2)/2

is the question correct?? none of the options seem to satisfy

here a>b since a/b is even integer

let a= 24 and b = 4.

A. a/2 = 12 => even B. b/2 = 2 => even C. (a+b)/2 = 14 => even D. (a+2)/2 = 13 => odd E. (b+2)/2 = 3 =>odd

now if a = 20 and b = 2 then a-b = 18 and a/b = 10 A. a/2 = 10 => even B. b/2 = 1 => odd C. (a+b)/2 = 11 => odd D. (a+2)/2 = 13 => odd E. (b+2)/2 = 2 => even

small correction : (a+2)/2 = 11 as a= 20 ,so 22/2= 11 not 13

Re: If a and b are positive integers such that a – b and a/b are [#permalink]
21 Jul 2014, 04:44

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. _________________

Re: If a and b are positive integers such that a – b and a/b are [#permalink]
26 Jul 2015, 21:56

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. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...