Question

If 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

Answer 1

$$n, p > 1 \\
5n = x^2\\
75np = x^3$$
Solve for n in terms of x:
$$n = \frac {x^2} 5$$
$$75(\frac{x^2} 5)p = x^3$$
Solve for p in terms of x:
$$15x^2p = x^3 \\
p = 15x$$
$$\frac{x^2} 5 + 15x = m$$
We wish to minimize \(m\).

Answer 2

C. 20

Answer 3

@bloopman your method is invalid

Answer 4

@TanteAnna, no, it isn't. I was about to use calculus to solve it, but because you were so kind to give him the answer I decided not to. Perhaps you should read the ToS before you give out another answer like that.

Answer 5

Ahaha! When you think that 5 and 75 are the same number your method is certainly invalid! Quit calling me out when you know you are wrong! How about you go read the ToS! @bloopman

Answer 6

No need to be aggressive. Please, do tell me where I stated 5 = 75.

Answer 7

5n=x275np=x3

Answer 8

That's where.

Answer 9

How is that saying 5 = 75?

Answer 10

Because you say x is the number in both equations but in the first equation we want 5 and in the second equation we want 75 so you are implying that 5 = x = 75 therefore 5 = 75. don't be a noob next time thanks

Answer 11

...

Answer 12

Lol'd.
10/10 if troll
7/10 if copypasta

Answer 13

You are the only troll here