Multiple

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billyr: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Tue Dec 16, 2008 11:53 pm

by billyr » Mon Feb 23, 2009 8:19 am

If n is a multiple of 5 and n=p^2*q, where p and q are prime numbers, which of the following must be multiple of 25?

a)p^2

b)q^2

c)p^2*q^2

d)pq

e)q^3

Thanks

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Source: Beat The GMAT — Problem Solving | Mon Feb 23, 2009 8:19 am

x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

Re: Multiple

by x2suresh » Mon Feb 23, 2009 8:24 am

billyr wrote:If n is a multiple of 5 and n=p^2*q, where p and q are prime numbers, which of the following must be multiple of 25?

a)p^2

b)q^2

c)p^2*q^2

d)pq

e)q^3

Thanks

n=p^2*q = 5k (p,q are prime numbers)
one of them must be 5. we don't know whether p=5 or q=5

p^2*q^2 --> ALWAYS MULTIPLE OF 25 (here it doesn't matter whether p=5 or q=5)

c

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welcome: Master | Next Rank: 500 Posts; Posts: 137; Joined: Thu Jan 08, 2009 1:27 am; Thanked: 7 times

by welcome » Mon Feb 23, 2009 12:29 pm

Say n=5k

as n=p^2 * q => 5K = p^2 * q (as p and q are prime, q should be 5, because k can not ve 5 otherwise 5K will make 5^2 but when you will make it equal to p^2 *q then q will be 1, which can not be 1 as a prime.)

so q^2 = 25 = > and B.

Shubham.
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590

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welcome: Master | Next Rank: 500 Posts; Posts: 137; Joined: Thu Jan 08, 2009 1:27 am; Thanked: 7 times

by welcome » Mon Feb 23, 2009 6:12 pm

Can you please post the OA.

Shubham.
590 >> 630 >> 640 >> 610 >> 600 >> 640 >> 590 >> 640 >> 590 >> 590

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