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

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

The tricky moment here is to notice that (5x)^2 has two different prime factors. The author does not mention the real number of prime factors. For example, the number 100 = 2*2*5*5, so has 4 prime factors, but it only has 2 distinct prime factors, 5 and 2.
So in this question, x can have the maximum of 2 prime factors, one can be something like 2,3,7 and the other 5 to maximize the possibilities of having prime factors.
_________________

Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.

X^2 is just a X multiplied by itself.
So it won't increase / decrease the number of prime factors.

for e.g 6 (6=2x3) has two prime factors
36 (36=2x2x3x3) also has two prime factors

Thus, # of prime factors always remains same for x, and x^2

Now coming to the question
5*X^2 has 2 prime factors
Thus 5*X will also have 2 prime factors
So, X can have at most 2 prime factors ( one of which'd be 5)
_________________

Everything is in flux, nothing stays still


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