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# Data Sufficiency

Author Message
Intern
Joined: 30 Jan 2018
Posts: 2

### Show Tags

31 Jul 2018, 08:19
00:00

Difficulty:

35% (medium)

Question Stats:

100% (01:16) correct 0% (00:00) wrong based on 6 sessions

### HideShow timer Statistics

If x and y are positive integers, is the product xy divisible by 9?
(1) The product xy is divisible by 6.
(2) x and y are perfect squares.

the answer is c for this

I have a doubt

Given information from the question stem: x and y are positive integers.
Statement 1: The product xy is divisible by 6. This tells you that 3 and 2 are factors
of xy. However this statement is not sufficient alone. Conceptual understanding
will tell you that if 3 is a factor of xy then it is possible that 9 is also a factor of
xy. However it is equally possible that 9 is not a factor of xy. If you are in doubt
you can use numbers and Play Devil’s Advocate. xy could equal 6 or 12, both
of which are divisible by 6 as the statement requires and are not multiples of 9.
This would yield an answer of “no.” xy could also equal 36, which is a multiple of
6 and also of 9. This would yield the answer of “yes.” Since yes and no answers
are both possible this statement is not consistent and is therefore not sufficient.
Eliminate choices A and D.
Statement 2: x and y are perfect squares. Conceptually this is clearly notsufficient. While each of the number must be a perfect square this statement
does not guarantee that the result will even be a multiple of 3, much less of 9.
Eliminate choice B.
Together: Statement 1 tells you that xy must include the prime factors of 2 and 3
(in order to be a multiple of 6). Since Statement 2 requires x and y to be perfect
squares the only way to have a 2 and a 3 as prime factors of x and y is to have
22 and 32 as factors of x and y. In fact, the smallest values for x and y are 4 and
9. So the answer to the question “Is xy divisible by 9?” is “yes.” Together the

but when we consider CWE CAN GET MULTIPLE VALUES SUCH AS 36,9 & 4,9AS WE ARE GETTING MULTIPLE VALUES SHOULDN'T THE ANSWER BEE

Math Expert
Joined: 02 Sep 2009
Posts: 52387

### Show Tags

31 Jul 2018, 08:29
AlphaAeon wrote:
If x and y are positive integers, is the product xy divisible by 9?
(1) The product xy is divisible by 6.
(2) x and y are perfect squares.

the answer is c for this

I have a doubt

Given information from the question stem: x and y are positive integers.
Statement 1: The product xy is divisible by 6. This tells you that 3 and 2 are factors
of xy. However this statement is not sufficient alone. Conceptual understanding
will tell you that if 3 is a factor of xy then it is possible that 9 is also a factor of
xy. However it is equally possible that 9 is not a factor of xy. If you are in doubt
you can use numbers and Play Devil’s Advocate. xy could equal 6 or 12, both
of which are divisible by 6 as the statement requires and are not multiples of 9.
This would yield an answer of “no.” xy could also equal 36, which is a multiple of
6 and also of 9. This would yield the answer of “yes.” Since yes and no answers
are both possible this statement is not consistent and is therefore not sufficient.
Eliminate choices A and D.
Statement 2: x and y are perfect squares. Conceptually this is clearly notsufficient. While each of the number must be a perfect square this statement
does not guarantee that the result will even be a multiple of 3, much less of 9.
Eliminate choice B.
Together: Statement 1 tells you that xy must include the prime factors of 2 and 3
(in order to be a multiple of 6). Since Statement 2 requires x and y to be perfect
squares the only way to have a 2 and a 3 as prime factors of x and y is to have
22 and 32 as factors of x and y. In fact, the smallest values for x and y are 4 and
9. So the answer to the question “Is xy divisible by 9?” is “yes.” Together the

but when we consider CWE CAN GET MULTIPLE VALUES SUCH AS 36,9 & 4,9AS WE ARE GETTING MULTIPLE VALUES SHOULDN'T THE ANSWER BEE

Discussed here: https://gmatclub.com/forum/if-x-and-y-a ... 06392.html In case of any further questions please post there.

Also, please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html
_________________
Re: Data Sufficiency &nbs [#permalink] 31 Jul 2018, 08:29
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