three different prime

[sanju09]

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



https://www.crushthetest.com

[mathbyvemuri]

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.

[amit28it]

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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