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# If x is a prime number, how many different factors has 18x?

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Intern
Joined: 20 Nov 2017
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Location: India
GRE 1: Q158 V150
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If x is a prime number, how many different factors has 18x?  [#permalink]

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29 Jul 2018, 00:30
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Difficulty:

55% (hard)

Question Stats:

55% (01:33) correct 45% (01:38) wrong based on 94 sessions

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If x is a prime number, how many different factors has 18x?

1. $$x^2$$ has 3 factors
2. $$x>3$$
Senior Manager
Joined: 22 Feb 2018
Posts: 391
Re: If x is a prime number, how many different factors has 18x?  [#permalink]

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29 Jul 2018, 00:58
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KarthikvsGMAT wrote:
If x is a prime number, how many different factors has 18x?

1. $$x^2$$ has 3 factors
2. $$x>3$$

OA: B
$$x$$ is prime, how many different factors are of $$18x$$?
$$18x = 2*3^2*x$$
Case 1: if $$x =2$$, then $$18x =36=2^2*3^2$$
then number of factors $$(2+1)(2+1)=9$$
Case 2: if $$x =3$$, then $$18x =54=2*3^3$$
then number of factors $$(1+1)(3+1)=8$$
Case 3: if $$x >3$$, then $$18x=2*3^2*x^1$$
then number of factors $$(1+1)(2+1)(1+1)=12$$

Statement 1 :$$x^2$$ has 3 factors
Square of every prime number has 3 factors: $$1,x,x^2$$
$$18 x$$ can have $$9,8$$ or $$12$$ factors depending on whether $$x =2,3$$ or $$x>3$$
So Statement 1 alone is not sufficient.

Statement 2: $$x>3$$
If $$x>3$$, then $$18x$$ will have $$12$$ factors.
So Statement 2 alone is sufficient.
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Re: If x is a prime number, how many different factors has 18x? &nbs [#permalink] 29 Jul 2018, 00:58
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