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Section - 24 Question - 20

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Section - 24 Question - 20

by camitava » Sat Sep 22, 2007 6:52 am
How to solve the prob? To me, A is coming as the answer. But OA is E.
Refer the question -
20. If n and p are different positive prime numbers, which of the integers , and np has (have) exactly 4 positive divisors?
(A) n4 only
(B) p3 only
(C) np only
(D) n4 and np
(E) p3 and np
Correct me If I am wrong


Regards,

Amitava
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by kajcha » Sat Sep 22, 2007 5:52 pm
Should be E

This is how I solved it.. (I prefer to substitute nos and try to eliminate the options)

assume n=2, p=3

np = 6 => divisors = 1,2,3,6

I assumed n4 is n^4 and p3 means p^3

n^4 = 16 => divisors 1,2,4,8,16 Does not satisfy question
P^3 = 27 => divisors 1,3,9,27

so np and p^3 have 4 divisors. Ans E
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