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Prime Numbers problem

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Junior | Next Rank: 30 Posts
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by divyalr » Wed Oct 07, 2009 6:19 am
Hi Folks,
I found this problem in the Advanced GMAT problems material. Please help solving it using a shortcut method.

Q> if p and q are primes, how many divisors does the product p^3.q^6 have?

Choices>
a) 8
b) 12
c) 18
d) 28
e) 36

Answer is d.
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by xcusemeplz2009 » Wed Oct 07, 2009 11:16 am
divisors will be
p^3=> 3 diff divisors
q^6=> 6 diff div
p^3*q^6=>18 diff div
and 1
adding 3+6+18+1=28

D is correct
It does not matter how many times you get knocked down , but how many times you get up
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Re: Prime Numbers problem

by aa2kash » Fri Oct 09, 2009 5:29 am
divyalr wrote:Hi Folks,
I found this problem in the Advanced GMAT problems material. Please help solving it using a shortcut method.

Q> if p and q are primes, how many divisors does the product p^3.q^6 have?

Choices>
a) 8
b) 12
c) 18
d) 28
e) 36

Answer is d.
@Divya
no of divisors is multiplication of (powers of each primes +1)

Here power of p is 3 and that of q is 6
No of divisors=(p+1)(q+1)=(3+1)(6+1)=28.
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