Which is an Integer?

Expert replies

dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Thu May 28, 2009 7:27 am

If (X,Y) is a solution to 6x+8y=33 then which of the following three could be an interger?

I X^1/2

II PX, where P is prime

III QY, where Q is even

A. I only
B. II Only
C I and III only
D II and III only
E. I, II and III

Like this post

Source: Beat The GMAT — Problem Solving | Thu May 28, 2009 7:27 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: Which is an Integer?

by Brent@GMATPrepNow » Thu May 28, 2009 7:58 am

dtweah wrote:If (X,Y) is a solution to 6x+8y=33 then which of the following three could be an interger?

I X^1/2

II PX, where P is prime

III QY, where Q is even

A. I only
B. II Only
C I and III only
D II and III only
E. I, II and III

If we want to know which of them "could" be an integer, then the answer is E.
The solution (4, 9/8) works for all three
1. 4^(1/2) = 2 (integer)
2. 4 multiplied by any prime number will yield an integer
3. if Q=8, then QY = 8(9/8)=9 (integer)

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

by mikeCoolBoy » Thu May 28, 2009 8:02 am

IMO D

we can rewrite the expression as

6x + 8y = 33 --> 8y = 33 - 6x ----> 8y = 3(11-2x)

we can see that y = 3 and x = 1.5 are in the line so

PX where P is prime, choosing P = 2 makes PX = 3 which is integer.
QY where Q is even, choosing Q = 2 makes QY = 6 which is an integer.
So II and III could be true.

8y is an even number
so we need 11 - 2x to be an even number so that the product of 3 and 11-2x is an even number.

11-2x has to be even ---> so 2x has to be odd which is impossible unless x is not an integer and therefore x ^ (1/2) cannot be an integer.

Choose D.

Like this post

mikeCoolBoy: Master | Next Rank: 500 Posts; Posts: 119; Joined: Tue Jan 20, 2009 10:16 pm; Thanked: 9 times; GMAT Score:730

by mikeCoolBoy » Thu May 28, 2009 8:50 am

You're completely right Bren, I wrongly assumed that Y was an integer complicating the problem.

Like this post

sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Sep 17, 2013 11:20 pm

i can see that a single word "could" has changed the entire question. we can prove all three to be true. what if we restrict the value of x and y to be only integers, does this effect the final answer?

Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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