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n and p are integers greater than 1 5n is the square of a number 75np

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n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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New post 22 May 2016, 13:55
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71% (01:53) correct 29% (02:35) wrong based on 155 sessions

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GMAT 1: 730 Q49 V40
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n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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New post 22 May 2016, 14:19
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1
3
\(n > 1\)
\(p > 1\)
\(5*n = x^2\)
\(75np = y^3\)
\(n+p = ?\)

Well, a square number is usually the result of himself times himself so in the case of n the least value possible (being 5 a prime) is 5*5
\(n=5\)
as for p
\(75*5*p= y^3\)
we know \(375\) is equal = \(5^3*3^1\) therefore to obtain a cube we need \(3^2\) or 9 -> \(p=9\)

\(p+n=14\)

A)
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Re: n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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New post 18 Jul 2017, 20:15
1
n and p are integers greater than 1; 5n is the square of a number; 75np is the cube of a number. The smallest value for n + p is

Given: 5n is the square of a number
This means that n=5\(a^2\), where a>=1

Given: 75np is the cube of a number
This means that 3*25*5\(a^2\)p is the cube of a number. This implies that p=\(3^2\)a

Now n+p = 5\(a^2\) + 9a = a [5a+9]

The smallest value of n+p, will be when a=1. Therefore, n+p = 5+9 = 14

Answer is A
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Re: n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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New post 07 Aug 2018, 05:01
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Re: n and p are integers greater than 1 5n is the square of a number 75np   [#permalink] 07 Aug 2018, 05:01
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