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01 Aug 2017, 01:23
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B
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55% (02:13) correct
45%
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wrong
based on 467
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(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
11 Jan 2018, 06:47
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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 , \(v^2 = s^3 * s^3 = s^6\)
=> \(v = s^3\)
=> number of factors of v = (3 + 1) = 4
=> Number of factors of v greater than 1 = (4 - 1) = 3
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 , \(v^2 = s^3 * s^3 = s^6\)
=> \(v = s^3\)
=> number of factors of v = (3 + 1) = 4
=> Number of factors of v greater than 1 = (4 - 1) = 3
General Discussion
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 16 Apr 2022
Posts: 527
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
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01 Aug 2017, 01:44
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Bunuel
(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
Let s & t be 2
2^6 = v^2
v = 2^3
v will have 4 divisors including 1
excluding 1 it will have 3
B
