DS - complex ds prob

goal_gmat · #1 (**permalink**) July 2nd, 2009, 06:36 AM

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Posted by: goal_gmat

pls help to explain the ds prob below

p^a * q^b * r^c * s^d = x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd

dori · #2 (**permalink**) July 2nd, 2009, 10:43 AM

IMO D

clerk · #3 (**permalink**) July 3rd, 2009, 08:27 AM

Second is sufficient, whereas the first is not
thus B

look, the prime integers can be distinct when and only when their powers are even. since the second says that the multiple of two powers has no 4 as a factor, we conclude that some of them are not even. if all of them were even, their multiple would have 4 as a factor, since two multiplied even integers can be divided by 4 evenly.
actually we can conclude that they are not distinct
understandable?

kooljoshi · #4 (**permalink**) July 19th, 2009, 09:29 AM

Clerk can u explain a bit more !!! i found the solution a bit cryptic...........

Quote:

Originally Posted by clerk

Second is sufficient, whereas the first is not
thus B

look, the prime integers can be distinct when and only when their powers are even. since the second says that the multiple of two powers has no 4 as a factor, we conclude that some of them are not even. if all of them were even, their multiple would have 4 as a factor, since two multiplied even integers can be divided by 4 evenly.
actually we can conclude that they are not distinct
understandable?

DS - complex ds prob

GMAT Math: Data Sufficiency (DS)