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# If x is a prime number, what is the number of different factors of 18x

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Intern
Joined: 18 Apr 2013
Posts: 33
If x is a prime number, what is the number of different factors of 18x  [#permalink]

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06 Jul 2017, 07:29
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57% (01:37) correct 43% (01:52) wrong based on 90 sessions

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If x is a prime number, what is the number of different factors of 18x?
1) x^2 has 3 factors
2) x>3
Senior Manager
Joined: 24 Apr 2016
Posts: 327
Re: If x is a prime number, what is the number of different factors of 18x  [#permalink]

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06 Jul 2017, 09:01
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If x is a prime number, what is the number of different factors of 18x?

18x can be written as 2 * 3^2 * x

Case 1: If x=2, then 18x = 2^2 * 3^2 , total number of factors = 3*3 = 9
Case 2: If x=3, then 18x = 2 * 3^3 , total number of factors = 2*4 = 8
Case 3: If x= a prime number other than 2 and 3, then 18x = 2 * 3^2 * x , total number of factors = 2*3*2 = 12

So we need to find out what is the value of x?

Statement 1) x^2 has 3 factors

Square of any Prime number will have 3 factors. Eg. 2^2, 3^2, 5^2. As this statement gives no new information. This statement is not sufficient.

Statement 2) x>3

This statement clearly tells us that x is greater than 3, which means the third case is applicable here.So the total number of factors = 12. This statement is sufficient.

Math Expert
Joined: 02 Aug 2009
Posts: 7764
If x is a prime number, what is the number of different factors of 18x  [#permalink]

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16 Jul 2018, 19:14
roastedchips wrote:
If x is a prime number, what is the number of different factors of 18x?
1) x^2 has 3 factors
2) x>3

the answer would depend on if x is a factor of 18, that is if x is 2 or 3
If x is 2 or 3, Ans will be different ..
a) x=2, 18*2=$$2^2*3^2....(2+1)(2+1)=3*3=9$$
b) X=3, 18*3=2*3^3.......(1+2)(3+1)=3*4=12
If x is any other prime number, Ans will be different.
$$18x=2*3^2*X.......(1+1)(2+1)(1+1)=2*3*2=12$$

1) $$x^2$$ has 3 factors.
Just tells us that $$x^2 is square of a prime number$$
Insufficient

2) X>3
now X is a prime number >3
Irrespective of the value of X, factors of 18x will be
18x=2*3^2*X
So factors are (1+1)(2+1)(1+1)=2*3*2=12
Sufficient

B
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If x is a prime number, what is the number of different factors of 18x   [#permalink] 16 Jul 2018, 19:14
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