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# If p is a prime number, how many positive factors of Y are not factors

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Math Expert
Joined: 02 Sep 2009
Posts: 52297
If p is a prime number, how many positive factors of Y are not factors  [#permalink]

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24 Apr 2018, 04:39
00:00

Difficulty:

85% (hard)

Question Stats:

28% (01:39) correct 72% (01:35) wrong based on 76 sessions

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If p is a prime number, how many positive factors of Y are not factors of X?

(1) X = 4p
(2) Y = 8p

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Re: If p is a prime number, how many positive factors of Y are not factors  [#permalink]

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24 Apr 2018, 05:03
1
Bunuel wrote:
If p is a prime number, how many positive factors of Y are not factors of X?

(1) X = 4p
(2) Y = 8p

Instead of solving explicitly, we'll use a few numbers to try generating contradictory solutions.
This is an Alternative approach.

(1), (2) give information about only one of X, Y so can't be sufficient.

Combined:
If we notice that both 4 and 8 are powers of 2, than a good guess would be that the question has something to do with powers of 2.
We'll try p = 2 and p = not 2, such as p = 3.
p = 2 gives X = 8, which has factors 1,2,4,8 and Y = 16 which has factors 1,2,4,8,16. In this case the difference in positive factors is 1.
p = 3 gives X = 12, which has factors 1,2,3,4,6,12 and Y = 24 which has factors 1,2,3,4,6,8,12,24. In this case the difference in positive factors is 2.
Insufficient!

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Re: If p is a prime number, how many positive factors of Y are not factors  [#permalink]

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11 May 2018, 22:14
Neither of statement alone is sufficient as individually they don't give info About X or Y

Combining both

Prime nos are all odd except 2

If we take 2
X=8=2^3 i.e. 4 factors
Y=16=2^4 i.e. 5 factors
Difference=5-4 =1

If any other prime p ..p is odd here
X=2^2*p
P has only 2 factors as it is prime
So x has 3*2=6 factors

Y has =2^3*p =4*2 = 8 factors
Difference=2

Since here we get 1 and 2 as difference between factors on taking different prices so combining is not yielding us result

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Re: If p is a prime number, how many positive factors of Y are not factors &nbs [#permalink] 11 May 2018, 22:14
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