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# How many different prime factors does x have?

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How many different prime factors does x have? [#permalink]

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13 Apr 2015, 21:18
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How many different prime factors does positive integer x have?

1) $$1 < x < 6$$

2) $$5x^2$$ has four factors

[Reveal] Spoiler: OA

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Last edited by Harley1980 on 14 Apr 2015, 05:02, edited 2 times in total.
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Re: How many different prime factors does x have? [#permalink]

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13 Apr 2015, 23:25
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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

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Retired Moderator
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Re: How many different prime factors does x have? [#permalink]

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14 Apr 2015, 04:19
VeritasPrepKarishma wrote:
Harley1980 wrote:
You must specify that x is an integer since you are talking about factors of x - otherwise a discussion on factors makes no sense.

I didn't know about such rule (
Thanks for clarification.
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Re: How many different prime factors does x have? [#permalink]

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17 Nov 2016, 15:54
Harley1980 wrote:
How many different prime factors does positive integer x have?

1) $$1 < x < 6$$

2) $$5x^2$$ has four factors

1. basically tells that: x can be 2,3,4,5 - either case, each of the numbers has only 1 distinct positive factor - sufficient.

2. has 4 factors - 5, x, x^2, and 5x^2 - thus, x is a prime number. sufficient.

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How many different prime factors does x have? [#permalink]

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10 Jan 2017, 06:26
Great Question.
Here is what i did in this one =>
We need the number of prime factors of the positive integer x.
Statement 1=>
x=>(1,6)=> x=2,3,4,5=> In each case => x will have just one prime factor=> Sufficient.
Statement 2=> The only value of x possible is 5.
Hence x will have only one factor. Sufficient

Hence D.

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Re: How many different prime factors does x have? [#permalink]

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31 Aug 2017, 01:28
VeritasPrepKarishma wrote:
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

Can you please explain why is it so?
If x is 5, number of factors will be (3+1) = 4 (this one is understandable, but why did you wite (3+1) - some rule?)
If x is a prime number other than 5, number of factors will be (1+1)(2+1) = 2*3 = 6
Re: How many different prime factors does x have?   [#permalink] 31 Aug 2017, 01:28
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