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If x, y and z are distinct prime numbers, how many positive factors do

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If x, y and z are distinct prime numbers, how many positive factors do  [#permalink]

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New post 21 Nov 2012, 08:07
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If x, y and z are distinct prime numbers, how many positive factors does (xy)^z have?

(1) z = 5

(2) x + y = 10

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Re: If x, y and z are distinct prime numbers, how many positive factors do  [#permalink]

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New post 21 Nov 2012, 08:19
1
A for me

Given that x,y and z are three distinct prime numbers
frm statement 1) z=5

so (xy)^5 = (x^5)*(y^5)
and so the no of positive factors is (5+1)*(5+1)=6*6=36

frm statement 2) x+y = 10
which means the possible combination is 3,7 or 7,3
if z=1 we have 4 factors
if z=2 we will have 9 factors and so on

so 2 is insufficient
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Re: If x, y and z are distinct prime numbers, how many positive factors do  [#permalink]

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New post 22 Nov 2012, 05:08
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If x, y and z are distinct prime numbers, how many positive factors does (xy)^z have?

\((xy)^z=x^z*y^z\). Now, since x and y are distinct prime numbers, then the number of factors equal to (z+1)(z+1) (check here: http://gmatclub.com/forum/math-number-theory-88376.html). Thus, all we need to know to answer the question is the value of z.

(1) z=5. Sufficient.

(2) x+y = 10. Not sufficient.

Answer: A.
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Re: If x, y and z are distinct prime numbers, how many positive factors do  [#permalink]

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New post 24 Nov 2012, 07:14
nice question !!

its A..

(z+1) (z+1)
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Re: If x, y and z are distinct prime numbers, how many positive factors do  [#permalink]

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Re: If x, y and z are distinct prime numbers, how many positive factors do   [#permalink] 20 Jan 2019, 04:28
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