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What is the smallest positive integer k such that the produc
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Updated on: 02 Feb 2020, 13:30
Updated on: 02 Feb 2020, 13:30
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What is the smallest positive integer k such that the product \(1575 \times k\) is a perfect square?
(A) 7
(8) 9
(C) 15
(D) 25
(E) 63
Kudos for the right answer and explanation
(A) 7
(8) 9
(C) 15
(D) 25
(E) 63
Kudos for the right answer and explanation
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Re: What is the smallest positive integer k such that the produc
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02 Feb 2020, 11:12
02 Feb 2020, 11:12
1
Carcass wrote:
What is the smallest positive integer k such that the product \(1575 * k\) is a perfect square?
(A) 7
(8) 9
(C) 15
(D) 25
(E) 63
Kudos for the right answer and explanation
(A) 7
(8) 9
(C) 15
(D) 25
(E) 63
Kudos for the right answer and explanation
Let us Factorize 1575: \(1575 = 5 * 315 = 5 * 5 * 63 = 25 * 9 * 7 = 5^2 * 3^2 * 7\)
Since we need to make \(1575 * k\) to become a perfect square, we need to multiply 1575 with 7 so that the resulting number has even powers of all its primes (a perfect square has even exponents of all its prime factors)
Thus, \(k = 7\)
\(Answer A\)
gmatclubot
Re: What is the smallest positive integer k such that the produc [#permalink]
02 Feb 2020, 11:12
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