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# If A is a positive integer less than 100

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If A is a positive integer less than 100  [#permalink]

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04 Feb 2016, 17:25
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If A is a positive integer less than 100, and $$\frac{7A}{30}$$ is an integer, then A has how many unique prime factors?

A) 2

B) 3

C) 5

D) 7

E) 8
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Joined: 02 Aug 2009
Posts: 8757
Re: If A is a positive integer less than 100  [#permalink]

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04 Feb 2016, 18:12
zxcvbnmas wrote:
If A is a positive integer less than 100, and $$\frac{7A}{30}$$ is an integer, then A has how many unique prime factors?

A) 2

B) 3

C) 5

D) 7

E) 8

Hi,
from $$\frac{7A}{30}$$ , we know A will be a multiple of 30..
Also a<100, so A can take values of 30,60,90..
irrespective of the value of A we take it will have the same unique prime factors..
so 30=2*3*5..
60=2^2*3*5..

so in all cases 2,3, and 5 are the unique prime factors..
ans is 3
B
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Re: If A is a positive integer less than 100  [#permalink]

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04 Feb 2016, 20:03
zxcvbnmas wrote:
If A is a positive integer less than 100, and $$\frac{7A}{30}$$ is an integer, then A has how many unique prime factors?

A) 2

B) 3

C) 5

D) 7

E) 8

for $$\frac{7A}{30}$$ to be an Integer, A must be a multiple of 30
i.e. A can be 30 or 60 or 90 only [in the range of less than 100]

If A=30 = 2*3*5 i.e. 3 prime factors
If A=60 = 2^2*3*5 i.e. 3 prime factors
If A=90 = 2*3^2*5 i.e. 3 prime factors

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Re: If A is a positive integer less than 100  [#permalink]

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16 Mar 2016, 08:28
Here from the question stem it is clear for 7A/30 to be an integer => A must be a multiple of 30...
Hence A=30,60 or 90=> all have 3 prime factors
hence B
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Re: If A is a positive integer less than 100  [#permalink]

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11 Feb 2020, 05:31
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Re: If A is a positive integer less than 100   [#permalink] 11 Feb 2020, 05:31