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

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Intern
Joined: 25 Dec 2018
Posts: 39
Location: India
Concentration: General Management, Finance
What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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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
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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03 Feb 2019, 01:05
1
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..
C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Math Expert
Joined: 02 Sep 2009
Posts: 52910
Re: What is the total number of positive factors of a? (1) 2a is a multip  [#permalink]

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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

PLEASE SEARCH: https://gmatclub.com/forum/what-is-the- ... 85001.html

TOPIC IS LOCKED AND ARCHIVED.
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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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# What is the total number of positive factors of a? (1) 2a is a multip

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