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GMATPrep Q: NEed help with second statement

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by nandinitaneja » Sun Aug 24, 2014 8:36 am
Hello,

For the question below, I derived that statement 1 is sufficient to show that x is a multiple of y, but am not sure how to think through statement 2. Any help would be much appreciated.

Thanks!


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by abhasjha » Sun Aug 24, 2014 9:11 am
(1)
y(3y + 7) = x
-- since y times some integer** is x, it follows that x is a multiple of y.
(** we know that 3y + 7 is an integer, because y is an integer)
sufficient

(2)
x(x - 1) is a multiple of y
-- could mean any of 3 things:
possibility a) x is a multiple of y
possibility b) x - 1 is a multiple of y
possibility c) neither x nor x - 1 is a multiple of y, but together they contain all the prime factors of y (e.g., x = 3, x - 1 = 2, y = 6)
insufficient, because we don't know whether it's possibility (a) or not

ANS A.
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by Brent@GMATPrepNow » Sun Aug 24, 2014 10:32 am
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)?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Aug 24, 2014 12:48 pm
HI nandinitaneja,

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

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Rich
Contact Rich at [email protected]
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by aukid411 » Mon Aug 25, 2014 12:22 am
thanks
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by Jim@StratusPrep » Mon Aug 25, 2014 3:39 am
I like to think of these as a fraction. This means that

(x^2 - x)/y is an integer.

Factoring you get this:

x(x-1)/y is an integer

You could plug numbers here, but generally speaking y could divide into x which would give you a 'yes' or y could divide into x-1 which would give you a 'no'
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