Data Sufficiency

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

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

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