If positive integer x is a multiple of 6 and positive : DS Archive
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# If positive integer x is a multiple of 6 and positive

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If positive integer x is a multiple of 6 and positive [#permalink]

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16 Mar 2005, 18:23
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If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?
(1) x is a multiple of 9.
(2) y is a multiple of 25.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Explain Pls
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16 Mar 2005, 19:13
"B"

state 1...X is multiple of 9 and 6 i.e. X is multuple of 18 (LCM of 9 and 6)

so X = 18n and Y = 14k

XY = 252K....if K = 10 then XY = 2520...then ans is YES, if K = 1, then NO
...insuff

state 2....Y is multiple of 25 and 14 i.e. Y is multiple of 350 (LCM of 25 and 14)

XY = 6*350(nk) = 2100(nk)...divisible by 105...suff
16 Mar 2005, 19:13
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