Harley1980 wrote:

How many different prime factors does x have?

1) \(1 < x < 6\)

2) \(5x^2\) has four factors

You must specify that x is an integer since you are talking about factors of x - otherwise a discussion on factors makes no sense.

Assuming x is an integer, each statement alone is sufficient.

1) \(1 < x < 6\)

x could be 2/3/4/5. In each case, it has only one distinct PRIME factor. We don't know the value of x but we know that it will have only one distinct prime factor. Sufficient

2) \(5x^2\) has four factors.

Number of factors of 5x^2 will depend on x.

If x is 5, number of factors will be (3+1) = 4

If x is a prime number other than 5, number of factors will be (1+1)(2+1) = 2*3 = 6

If x is a composite number, number of factors will be even more.

Since number of factors is 4, x must be 5 and has one distinct prime factor. Sufficient

Answer (D)

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