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Re: If s and t are both primes, how many positive divisors [#permalink]
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Re: If s and t are both primes, how many positive divisors [#permalink]
what does "bump for further discussion" mean?
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Re: If s and t are both primes, how many positive divisors [#permalink]
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When a question (usually a good one) is buried somewhere on the board but it is worth "bump for further discussion" brings up it among the most recent posts to the students' attention.

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Re: If s and t are both primes, how many positive divisors [#permalink]
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soumya1989 wrote:
Given \((s^3)(t^3) = v^2\) .If s and t are both primes, how many positive divisors of v are greater than 1, if v is an integer?

(A) two

(B) three

(C) five

(D) six

(E) eight


Given: V is an integer => \(\sqrt{S^3 * T^3}\) => must be an integer

but given S and T are prime numbers, then \(\sqrt{S^3 * T^3}\) cannot be an integer, unless and until both the primes are same.

for V to be an integer, S = T , \(V^2 = S^3 * S^3 = S^6\); \(\sqrt{ V^2 }\) = \(\sqrt{(S^3)^2}\)
=> \(V = S^3\)
=> number of factors of V = (3 + 1) = 4 (rules)
=> Number of factors of V greater than 1 = (4 - 1) = 3

#Reference GMATCLUB.

https://youtu.be/aUTz3b5kgfY
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Re: If s and t are both primes, how many positive divisors [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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