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If 5x^2 has two different prime factors, at most how many di

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If 5x^2 has two different prime factors, at most how many different prime factors does x have?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Nov 2013, 08:26, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If 5x^2 has two different prime factors, at most how many di [#permalink]

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New post 14 Nov 2013, 12:07
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suprememodelrus wrote:
If 5x^2 has two different prime factors, at most how many different prime factors does x have?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.

Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors).

Answer: B.
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Re: If 5x^2 has two different prime factors, at most how many di [#permalink]

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New post 13 Feb 2014, 03:07
A little bit more explaination:
5x^2 has 2 prime factors.
One of them has to be 5 (since 5 is a factor of 5x^2 and 5 is prime).

Since the question asks for maximum no of prime factors that x can have, the answer has to be 2 (One of the two prime nos has to be 5, like x can be 10 or 15 or 20 ...etc, with 5 along with 2 0r 3 as the other prime factor)
The other factor is not known to us.

Moreover, since the question says 5x^2 has two different prime factors, x must have atleast one factor other than 5
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Re: If 5x^2 has two different prime factors, at most how many di [#permalink]

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Re: If 5x^2 has two different prime factors, at most how many di [#permalink]

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New post 13 Oct 2016, 10:41
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Re: If 5x^2 has two different prime factors, at most how many di [#permalink]

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New post 14 Jan 2017, 00:14
Properties in action->
1->When we multiply a positive integer x with another positive integer n,the number of prime factors of nx may be equal to x or greater than x.
2->\(X\) and \(X^n\) always have the exact same prime factors.
Case 1
In this case since 5x^2 has 2 prime factors.
So x can have one prime factors => and that will not be 5 so that 5x^2 has two primes.
OR
Case 2
In this case x can have two prime factors including 5 => e.g => x=5*3 => 5x^2=> 2 prime factors.
Hence At the most -> x can have 2 prime factors.


Hence B.

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Re: If 5x^2 has two different prime factors, at most how many di   [#permalink] 14 Jan 2017, 00:14
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