If x and y are integers greater than 1, is x a multiple of y?
(a) 3y^2 + 7y = x
(b) x^2 - x is a multiple of y
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singhmaharaj
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Brent@GMATPrepNow
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Target question: Is x a multiple of y?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
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
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Amrabdelnaby
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I have a question pertaining to statement 2.
I actually considered it sufficient without even doing any calculations because I applied the following rule backwards.
If K is a divisor of M, and K is a divisor of N, then K is a divisor of M+N, M-N, and N-M.
Now since it appears to be that statement 2 is insufficient, here comes my question:
If K is a divisor of M-N, it doesn't necessarily entail that K is a divisor of M and a divisor of N? In other words, can we not apply the above mention rule backwards or am I missing something here?
Please advise.
I actually considered it sufficient without even doing any calculations because I applied the following rule backwards.
If K is a divisor of M, and K is a divisor of N, then K is a divisor of M+N, M-N, and N-M.
Now since it appears to be that statement 2 is insufficient, here comes my question:
If K is a divisor of M-N, it doesn't necessarily entail that K is a divisor of M and a divisor of N? In other words, can we not apply the above mention rule backwards or am I missing something here?
Please advise.
Brent@GMATPrepNow wrote:Target question: Is x a multiple of y?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
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
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DavidG@VeritasPrep
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No. You can see this with simple numbers. Say M = 9 and N = 7. 9 - 7 = 2, so we can set K equal to 2. Clearly, 2 is not a divisor of either 9 or 7. (And a reminder that just because x --> y does not necessarily mean that y --> x.)If K is a divisor of M-N, it doesn't necessarily entail that K is a divisor of M and a divisor of N? In other words, can we not apply the above mention rule backwards or am I missing something here?
