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X multiple of Y

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X multiple of Y

by lukaswelker » Tue Apr 08, 2014 10:00 am
Hey Guys

I can't seem to find a logical way to resolve this question;

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

Any tips?

Many thanks
Lukas
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Apr 08, 2014 1:40 pm
lukaswelker wrote: 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
Brent Hanneson - Creator of GMATPrepNow.com
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