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If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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20 Mar 2018, 23:19
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Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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21 Mar 2018, 00:49
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IMO D 5880 = 2^3 * 7^2 * 3 * 5 Therefore, to make it a perfect square, the minimum value of k should be = 2 * 3 * 5 = 30 Thus, D. Sent from my Lenovo K53a48 using GMAT Club Forum mobile app



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Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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21 Mar 2018, 02:32
Bunuel wrote: If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?
(A) 2 (B) 6 (C) 15 (D) 30 (E) 140 Bunuel there seems something wrong with the question. Is the integer at hand 5,880*k or 5,880k which is a concatenation of 5,880 & k. Is this an ambiguity or am I making a mistake in reading it properly. Please advise. Best, Gladi



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Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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21 Mar 2018, 02:46
Gladiator59 wrote: Bunuel wrote: If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?
(A) 2 (B) 6 (C) 15 (D) 30 (E) 140 Bunuel there seems something wrong with the question. Is the integer at hand 5,880*k or 5,880k which is a concatenation of 5,880 & k. Is this an ambiguity or am I making a mistake in reading it properly. Please advise. Best, Gladi 5,880k is 5,880*k, so 5,880 multiplied by k (also recall that multiplication sign is often omitted). It cannot be a fivedigit integer 5880k because if it were it would have been explicitly mentioned.
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Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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22 Mar 2018, 15:47
Bunuel wrote: If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?
(A) 2 (B) 6 (C) 15 (D) 30 (E) 140 We are given that 5,880k is a perfect square. We must remember that all perfect squares break down to unique prime factors, each of which has an exponent that is a positive multiple of 2. So, let’s break down 5,880 into its prime factors to determine the minimum value of k. 5,880 = 588 x 10 = 12 x 49 x 10 = 2^3 x 3^1 x 5^1 x 7^2 So, in order for 5,880k to be a perfect square, k must contain the factors 2 x 3 x 5 = 30 (so that 5,880k = 2^4 x 3^2 x 5^2 x 7^2), so 30 is the smallest possible value of k. Answer: D
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If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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25 Mar 2018, 13:31
Solution • \(5880* k\) can be written in prime factorization form as \(2^3 * 3 *5 * 7^2 * k\).
• Since \(5880 * k\) is a perfect square, hence \(5880 * k=n^2\), where \(n\) is any integer. o \(n^2 = 2^3 * 3 * 5 * 7^2 * k\)
o After taking square root on both the sides, we can write: o \(n= 2*7* \sqrt{(2*3*5*k)}\) oFor \(n\) to be an integer,\(\sqrt{(2 * 3 * 5 * k)}\) must be a perfect square. oHence,\(k = 2 * 3 * 5 *\) (square of any positive integer) . • The least possible value of the square of a positive integer is 1. o Hence, k=2 * 3 * 5 = 30 . Answer: D
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Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]
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26 Mar 2018, 00:22
Bunuel wrote: If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?
(A) 2 (B) 6 (C) 15 (D) 30 (E) 140 The rule says, " A perfect square always has even number of powers of prime factors". Prime factorisation of 5880 = 2^3*3^1*5^1*7^2 Therefore, to make 5880 a perfect square we need to multiply it by a set of 2*3*5 = 30 Hence (D)
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