Which is odd?

Expert replies

erjamit: Master | Next Rank: 500 Posts; Posts: 170; Joined: Mon Oct 22, 2007 4:36 am; Thanked: 7 times

by erjamit » Tue Jul 29, 2008 6:56 am

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

OA D

https://www.urch.com/forums/gmat-problem ... 16odd.html

I am not sure whether choices are correct since all choices seem to be wrong to me..

Thanks
Amit

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jul 29, 2008 6:56 am

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Which is odd?

by Ian Stewart » Tue Jul 29, 2008 7:41 am

erjamit 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

You can see that A, B, C and E can all be even by trying a = 8, b = 4 for A, B and C, and a = 8, b = 2 for E. So by elimination, D must be correct. We can prove this:

If a/b is even, then a must be even. If a is even and a - b is even, then b must also be even. So a, b and a/b are all even; a/b = x, or a = bx, where b and x are both even. So a is the product of two even numbers; a must be divisible by 4. Now look at answer D:

(a+2)/2 = (a/2) + 1

We know a/2 is even, since a is a multiple of 4. So a/2 + 1 is even + odd = odd.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

erjamit: Master | Next Rank: 500 Posts; Posts: 170; Joined: Mon Oct 22, 2007 4:36 am; Thanked: 7 times

by erjamit » Tue Jul 29, 2008 8:54 am

Thanks Ian. It makes sense.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review