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# How many prime factors does N have?

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Re: How many prime factors does N have? [#permalink]
Why statement 1 is sufficient? is because of 2?
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Re: How many prime factors does N have? [#permalink]
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we need to check for factors only upto $$\sqrt{n}$$ because the factors repeat after this. See attached file
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2018_10_30 08_26 Office Lens.jpg [ 98.8 KiB | Viewed 2770 times ]

jorgetomas9 wrote:
Why statement 1 is sufficient? is because of 2?
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Re: How many prime factors does N have? [#permalink]
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

Stmt 2 is obviously sufficient

let's look at stmt 1:

In GMAT world we don't have sq rt of -ve numbers ... thus we will consider only whole numbers.

0 and 1 are out of commission because they don't have prime factors.

2 --> least prime factor pf 2 is 2 which is greater than sq rt of 2 i.e. 1.41
3 and other prime numbers --> same as 2
4 --> least prime factor = sq rt of 4 = 2 .... this doesn't satisfy our condition ... thus we can't consider 4

For all even numbers > 4, least prime factor = 2 will be lesser than sq rt of that number thus we can't consider those numbers

9 --> least prime factor = sq rt of 9 = 3 .... this doesn't satisfy our condition ... thus we can't consider 9

Next odd non prime number = 15 --> least prime number = 3 which is lesser than sq rt of 15 .... thus we can't consider odd non prime numbers ....

This leaves us with ONLY PRIME NUMBERS.

This is sufficient to answer our question.

I hope that helps!
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Re: How many prime factors does N have? [#permalink]
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

Either statement suggests that N is prime.

D
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Re: How many prime factors does N have? [#permalink]
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

1. Imagine, this is possible only when the greatest prime factor is the prime number itself. Hence, N is a prime number and has only 1 prime factor- N itself.

2. This is possible only for a prime number. Only a prime number has 2 factors. Any prime number has one prime factor (the number itself). Hence, the answer is 1. Sufficient.

D.
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Re: How many prime factors does N have? [#permalink]
Aamirso wrote:
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

Either statement suggests that N is prime.

D

Hi,

Please try to post meaningful posts. The option D in DS questions means that both the statements are individually sufficient to answer the question.

Best.

Posted from my mobile device
Re: How many prime factors does N have? [#permalink]
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