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# If p is a positive integer, what is total number of positive factors

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Director
Joined: 02 Oct 2017
Posts: 727
If p is a positive integer, what is total number of positive factors  [#permalink]

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08 Jul 2018, 03:00
1
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:41) correct 46% (01:41) wrong based on 28 sessions

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If p is a positive integer, what is total number of positive factors of 10p

(1) p has total of 3 positive factors

(2) The greatest common factor of 10 and p is 1

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Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: If p is a positive integer, what is total number of positive factors  [#permalink]

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08 Jul 2018, 04:39
push12345 wrote:
If p is a positive integer, what is total number of positive factors of 10p

(1) p has total of 3 positive factors

(2) The greatest common factor of 10 and p is 1

Positive factors of 10p will depend on value of p or atleast number and type of factors of p

1) p has 3 positive factors.
It tells us that p is a square of prime number.
If p contains the prime factor same as 10 has that is 2 or 5, answer will be different from when prime factor of p is not 2 or 5
Say 2.. 10p=10*2^2=2^3*5.....# of factors = (1+1)(3+1)=8
Say 7.. 10p=$$10*7^2=2*5*7^2$$....# of factors=(1+1)(1+1)(2+1)=2*2*3=12
Insufficient

2) GCF of 10 and p is 1
So p and 10 do not have any common factor...
Value of p required.
Insufficient

Combined..
p does not have 2 or 5..
Ans 12
Sufficient

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

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Re: If p is a positive integer, what is total number of positive factors &nbs [#permalink] 08 Jul 2018, 04:39
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