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# If x and y are integers and xy = 660, x or y must be divisible by whic

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Math Expert
Joined: 02 Sep 2009
Posts: 51071
If x and y are integers and xy = 660, x or y must be divisible by whic  [#permalink]

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19 Apr 2016, 02:04
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:28) correct 24% (01:18) wrong based on 129 sessions

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If x and y are integers and xy = 660, x or y must be divisible by which of the following?

A. 3
B. 4
C. 6
D. 20
E. 30

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Re: If x and y are integers and xy = 660, x or y must be divisible by whic  [#permalink]

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19 Apr 2016, 04:59
1
xy = 660 = 2 * 2 * 3 * 5 * 11

660 is even and a multiple of 3 --> So x or y must be a multiple of 3.

Let's check it out:
Consider 660 = 2 * 330 --> x or y cannot be a multiple of 4, 20
Consider 660 = 4 * 165 --> x or y cannot be a multiple of 6, 30

Math Expert
Joined: 02 Aug 2009
Posts: 7098
Re: If x and y are integers and xy = 660, x or y must be divisible by whic  [#permalink]

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19 Apr 2016, 05:20
2
1
Bunuel wrote:
If x and y are integers and xy = 660, x or y must be divisible by which of the following?

A. 3
B. 4
C. 6
D. 20
E. 30

Vyshak a good solution..
The reasoning is that the solution has to be a PRIME number because any other composite number can be expressed in terms which may not necessarily contain that composite number..
example 36 may be 6*6 BUT 36 can still be expressed in PRODUCT of factors that may not contain..
36 = 4*9..

so a solution would bea prime factor of 660..
here 3 is given
A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 10 Apr 2016
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Re: If x and y are integers and xy = 660, x or y must be divisible by whic  [#permalink]

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19 Apr 2016, 09:38
Just using prime factorization or normal factorization will easily tell you its going to be a multiple of 3

330 times 2
55 times 12
etc
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Re: If x and y are integers and xy = 660, x or y must be divisible by whic  [#permalink]

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31 Jul 2018, 22:18
I don't completely understand why it needs to be divisible by 3 and why it can't be divisible by 4 i.e. 2^2, which is also contained in the prime factorisation.

Anyone able to clarify?
Re: If x and y are integers and xy = 660, x or y must be divisible by whic &nbs [#permalink] 31 Jul 2018, 22:18
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