three different prime

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed May 02, 2012 3:43 am

The positive integer x is a product of three different prime numbers, p, q, and r. If r > q > p, which of the following must be true?

I. The greatest prime number that is a factor of x is r.
II. If p > 5 then x is not divisible by 5.
III. x^2 is divisible by p, q, and r.

(A) III, only
(B) I and II, only
(C) I and III, only
(D) II and III, only
(E) I, II, and III

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Source: Beat The GMAT — Problem Solving | Wed May 02, 2012 3:43 am

mathbyvemuri: Master | Next Rank: 500 Posts; Posts: 142; Joined: Thu Apr 26, 2012 3:24 am; Location: India; Thanked: 28 times

by mathbyvemuri » Wed May 02, 2012 11:30 pm

All are correct, hence answer is option "E"
explanation:
As x can be expressed as the product of three primes p,q,r, where r is the greatest of the three,
statement I is directly implied.
If p>5, q and r must also be greater than 5 and hence there is no scope of 5 to be a factor and hence statement II is correct.
As x is divisible by p,q and r, x^2 is also divisible by them and hence statement III is correct.

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amit28it: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Fri Nov 04, 2011 12:35 amFollowed by: 2 members

by amit28it » Thu May 03, 2012 12:00 am

First of all its a nice question and I have just completed its solution and the answer is E same given by mathbyvemuri and continue to post these kind of skillful questions.
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