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Director  Joined: 16 May 2014
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If s and t are both primes, how many positive divisors [#permalink]
Expert's post 00:00

Question Stats: 41% (00:46) correct 58% (01:22) wrong based on 43 sessions
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
[Reveal] Spoiler: OA

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If you find this post helpful, please press the kudos button to let me know !  Intern Joined: 18 Jun 2014
Posts: 39
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Kudos [?]: 30  , given: 15

Re: GRE Math Challenge #3 [#permalink]
1
KUDOS
s,t = 2 and v = 8. Positive divisors greater than 1 = {2,4,8}.
Therefore, answer would be three (B)
Manager  Joined: 06 Jun 2018
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Re: GRE Math Challenge #3- Solve (s^3)(t^3) = v^2 [#permalink]
soumya1989 wrote:
Level 170 question

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

Tough one. Nice question. Tricky.

Note :

if we add 1 to the exponents of each primes and multiply them we get the total number of factors including 1 and the number itself.

Total factor : (3+1) (3+1) = 16.

Remember that 16 is the factor of $$v^2$$. So, v has 4 factors for sure as v's factors was squared.

So, v has 4 factors.

Now , it's stated in the question that we need to find out the number of divisors of v that are greater than 1. In our factor calculation we consider 1 too. So it's time to deduct now.

Total number of factors greater than 1 = 4-1 = 3.

Founder  Joined: 18 Apr 2015
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Re: If s and t are both primes, how many positive divisors [#permalink]
Expert's post
Bump for further discussion
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Intern Joined: 11 Dec 2019
Posts: 29
Followers: 0

Kudos [?]: 2 , given: 19

Re: If s and t are both primes, how many positive divisors [#permalink]
what does "bump for further discussion" mean? Founder  Joined: 18 Apr 2015
Posts: 13357
Followers: 288

Kudos [?]: 3391  , given: 12192

Re: If s and t are both primes, how many positive divisors [#permalink]
2
KUDOS
Expert's post
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.

Regards
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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Director  Joined: 22 Jun 2019
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Re: If s and t are both primes, how many positive divisors [#permalink]
1
KUDOS
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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