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What is the total number of positive factors of a? (1) 2a is a multip

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What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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New post 02 Feb 2019, 08:19
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What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.



Kudos for every explanation :)
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Re: What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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New post 03 Feb 2019, 01:05
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mangamma wrote:
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.



Kudos for every explanation :)


What is the total number of positive factors of a?

(1) 2a is a multiple of 50.
We do not know what is 2a..
It can be 50, that is 2a=50...a=25=5^2....prime factors is (2+1)=3
Say 2a is 100, that is 2a=100....\(a=50=2*5^2\). Factors is (1+1)(2+1)=2*3=6
Insufficient.

(2) a/9 is an integer and has exactly 3 positive factors.
This means a/9 is square of a prime number..
Let \(\frac{a}{9}=9.....a=81=3^4\).. factors =(4+1)=5
Let \(\frac{a}{9}=4.....a=36=3^2*2^2\).. factors =(2+1)(2+1)=3*3=9
Different answers, so insufficient..

Combined..
a is a multiple of 25.. but \(\frac{√a}{3}\) is a prime number..
So only possible value is 25*9..
Factors of \(5^23^2\) are (2+1)(2+1)=9..
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Re: What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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New post 03 Feb 2019, 01:08
mangamma wrote:
What is the total number of positive factors of a?

(1) 2a is a multiple of 50.

(2) a/9 is an integer and has exactly 3 positive factors.



Kudos for every explanation :)


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Re: What is the total number of positive factors of a? (1) 2a is a multip   [#permalink] 03 Feb 2019, 01:08
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