Data Sufficiency

If x and y are integers greater than 1, is x a multiple of y?
(1) 3y² + 7y = x
(2) x² - x is a multiple of y

Target question: Is x a multiple of y?
Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
For example, 12 is a multiple of 3 because 12 = (3)(4)
So, let's rephrase the question as...
REPHRASED target question: Does x = (y)(some integer)?

Statement 1: 3y² + 7y = x
Factor to get x = y(3y + 7)
If y is an integer, then (3y + 7) must be an integer
In other words: x = y(some integer)
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x² - x is a multiple of y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case, x IS a multiple of y
Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case, x is NOT a multiple of y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Hi april24,

This DS question is a great "concept" question. With some Number Property knowledge and a bit of TESTing VALUES, you can get to the answer without doing too much work.

We're told that X and Y are both INTEGERS GREATER THAN 1. We're asked if X is a multiple of Y. This is a YES/NO question.

Fact 1: 3Y² + 7Y = X

There's a great Number Property rule that applies here: If a multiple of some number is added to another multiple of the same number, then the total will ALSO be a multiple of that original number.

For example...
4 is a multiple of 2
8 is a multiple of 2
So....4+8 = 12 is a multiple of 2

We know that Y is an INTEGER....
3Y² is a multiple of Y
7Y is a multiple of Y
So... 3Y² + 7Y is a multiple of Y

Since X = 3Y² + 7Y, we know that X MUST be a multiple of Y. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: X² - X is a multiple of Y

Here, let's TEST Values....
If X = 4
4² - 4 = 12
12 is a multiple of Y, so Y could be 2, 3, 4 or 6
If Y = 2, then the answer to the question is YES
If Y = 3, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich