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22 May 2016, 13:55
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:57) correct
28%
(02:35)
wrong
based on 253
sessions
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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
A. 14
B. 18
C. 20
D. 30
E. 50
5n is the square of a number;
75np is the cube of a number.
The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50
DensetsuNo
Joined: 11 Oct 2015
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Posts: 88
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Schools: HBS 2+2 '22 MIT Sloan MSMS"18
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22 May 2016, 14:19
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\(n > 1\)
\(p > 1\)
\(5*n = x^2\)
\(75np = y^3\)
\(n+p = ?\)
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)
\(p > 1\)
\(5*n = x^2\)
\(75np = y^3\)
\(n+p = ?\)
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)
General Discussion
18 Jul 2017, 20:15
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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
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
