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Math Expert V
Joined: 02 Sep 2009
Posts: 56266
n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (01:53) correct 29% (02:35) wrong based on 155 sessions

### HideShow timer Statistics 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

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Manager  Status: 2 months to go
Joined: 11 Oct 2015
Posts: 110
GMAT 1: 730 Q49 V40 GPA: 3.8
n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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3
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)
##### General Discussion
Senior Manager  G
Joined: 24 Apr 2016
Posts: 327
Re: n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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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

Non-Human User Joined: 09 Sep 2013
Posts: 11667
Re: n and p are integers greater than 1 5n is the square of a number 75np  [#permalink]

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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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