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Updated on: 19 Aug 2019, 02:57
Originally posted by garcmillan on 19 Aug 2019, 02:30.
Last edited by Bunuel on 19 Aug 2019, 02:57, edited 1 time in total.
Last edited by Bunuel on 19 Aug 2019, 02:57, edited 1 time in total.
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C
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If n is the smallest integer such that 216 times n is the square of an integer, what is the value of n?
(A) 1
(B) 2
(C) 6
(D) 12
(E) 24
(A) 1
(B) 2
(C) 6
(D) 12
(E) 24
19 Aug 2019, 03:00
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garcmillan
\(216 = 2^3*3^3\).
For 216*n to be a perfect square (so the square of an integer), n must complete odd powers of primes in 216 to even powers. So, the least positive integer n, for which 216*n is a perfect square is 2*3 = 6.
Answer: C.
Similar question: https://gmatclub.com/forum/if-n-is-the- ... 93707.html
19 Aug 2019, 03:10
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Every prime factor in a square number will be repeated and will be in pairs.
216 = 2 * 2 * 2 * 3 * 3 * 3
We see that one 2 and one 3 don't have a pairing partner.
So, 2 * 3 will make it a perfect square.
Thus, we can have
2 * 2 * 2 * 2 * 3 * 3 * 3 * 3
Hence, n = 2 * 3 = 6
Answer C
216 = 2 * 2 * 2 * 3 * 3 * 3
We see that one 2 and one 3 don't have a pairing partner.
So, 2 * 3 will make it a perfect square.
Thus, we can have
2 * 2 * 2 * 2 * 3 * 3 * 3 * 3
Hence, n = 2 * 3 = 6
Answer C
