DS:Greatest common factor & least common multiple(gmatpr : DS Archive
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# DS:Greatest common factor & least common multiple(gmatpr

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Manager
Joined: 12 Jul 2006
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DS:Greatest common factor & least common multiple(gmatpr [#permalink]

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16 Jul 2006, 11:20
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100% (01:16) correct 0% (00:00) wrong based on 3 sessions

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If x and y are positive integers, what is the value of xy?

a) The greatest common factor of x and y is 10
b) The least common multiple of x and y is 180

Thanks
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Good is the greatest enemy of great.

Manager
Joined: 04 Jul 2006
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16 Jul 2006, 12:18
C.

Each statement alone is not sufficient (pretty obvious).

Both statements together are sufficient. x=10 and y=180 are the only numbers that fulfill both properties.
(1) states that 10 is a common factor (and that it is the largest common factor). Therefore x and y must be multiples of 10.

Because of (2) we need to consider the factors of 180, that are multiples of 10. These are 10, 30, 60, 90 and 180. The least common multiple of two of these numbers is always lower than 180, except for 10 and 180 (easy to check) .

Therefore only 10 and 180 fulfill both properties.
Manager
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16 Jul 2006, 12:37
Quote:
HCF (x, y) * LCM (x, y) = x * y

... true.

Nice formula - thanks!
Manager
Joined: 12 Jul 2006
Posts: 67
Location: Boston
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Kudos [?]: 5 [0], given: 0

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17 Jul 2006, 08:13
Thank you guys. C is the correct answer.
_________________

Good is the greatest enemy of great.

17 Jul 2006, 08:13
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