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GRE 1: Q165 V161
If s and t are both primes, how many positive divisors
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06 Aug 2014, 14:03
06 Aug 2014, 14:03
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Question Stats:
43% (01:03) correct
56% (01:41) wrong based on 64 sessions
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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
(A) two
(B) three
(C) five
(D) six
(E) eight
Re: GRE Math Challenge #3
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06 Aug 2014, 23:58
06 Aug 2014, 23:58
1
s,t = 2 and v = 8. Positive divisors greater than 1 = {2,4,8}.
Therefore, answer would be three (B)
Therefore, answer would be three (B)
Re: GRE Math Challenge #3- Solve (s^3)(t^3) = v^2
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17 Jul 2018, 15:04
17 Jul 2018, 15:04
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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
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.
The correct answer is B.
