BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is y an integer?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Thu Aug 28, 2014 9:29 am

Is y an integer?

by mkramer » Wed Sep 24, 2014 5:41 pm
Can someone help me determine why selection (1) is sufficient? When I'm doing the problem I believe x could be three, making y = 0 so it would actually be insufficient?

If x is an integer, is y an integer?

(1) (4x + 4y)/2 = 6
(2) (3x + 6y)/3 = 5

In selection (1), you can simplify the expression to be x + y = 3. If this is the case, x can be 1, 2, or 3 since x must be an integer. BUT, this makes y either 0, 1, or 2. Since y can be 0, statement (1) is insufficient, correct? The service I'm using said I was wrong and statement (1) is sufficient.

Would appreciate any input.

Thanks
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 24, 2014 5:49 pm
mkramer wrote:
If x is an integer, is y an integer?

(1) (4x + 4y)/2 = 6
(2) (3x + 6y)/3 = 5
Target question: Is y an integer?

Given: x is an integer

Statement 1: (4x + 4y)/2 = 6
Multiply both sides by 2 to get: 4x + 4y = 12
Divide both sides by 4 to get: x + y = 3
Since x is an INTEGER and 3 is an INTEGER, we can rewrite the above equation as INTEGER + y = INTEGER
From this, we can conclude that y must be an integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (3x + 6y)/3 = 5
Multiply both sides by 3 to get: 3x + 6y = 15
Divide both sides by 3 to get: x + 2y = 5
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 2, in which case y IS an integer
Case b: x = 2 and y = 1.5, in which case y is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Sep 24, 2014 5:52 pm, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 24, 2014 5:52 pm
mkramer wrote:Can someone help me determine why selection (1) is sufficient? When I'm doing the problem I believe x could be three, making y = 0 so it would actually be insufficient?

If x is an integer, is y an integer?

(1) (4x + 4y)/2 = 6
(2) (3x + 6y)/3 = 5

In selection (1), you can simplify the expression to be x + y = 3. If this is the case, x can be 1, 2, or 3 since x must be an integer. BUT, this makes y either 0, 1, or 2. Since y can be 0, statement (1) is insufficient, correct? The service I'm using said I was wrong and statement (1) is sufficient.

Would appreciate any input.

Thanks
First, the question does not say that x and y are POSITIVE integers.
So, if x + y = 3, there are infinitely many solutions, such as x=1 & y=2, x=-1 & y=4, x=3 & y=0, x=11 & y=-8, etc

Second, 0 IS an integer.
Integers are as follows: ...-4, -3, -2, -1, 0, 1, 2, 3, 4, ....

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Sep 24, 2014 9:04 pm
Hi mkramer,

Brent has properly explained the solution to this DS question, so I won't rehash that here.

Number Properties (the little rules behind how math "works") are a big part of the GMAT and you'll actually see them in many DS questions, so you have be clear on the explicit definitions of all Number Property vocabulary words. The good news is that the definitions are pretty straight-forward.

Here, the issue is "integer" vs. "non-integer" - in essence, is Y a WHOLE NUMBER or NOT?

Integers can be positive (1, 2, 3, etc.), negative (-1,-2,-3, etc.) or 0. This definition has NOTHING to do with positive/negative nor odd/even.

In these types of prompts, I always take lots of little notes on the pad, so I don't forget what I've been GIVEN and what I'm trying to figure out. With enough practice, you'll find Number Property questions to be pretty easy (they're all beatable by TESTing VALUES) and if you can spot the patterns when they show up, you'll be able to answer these questions quickly too.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1