Question

10. 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...

Answer 1

don't you have a textbook from class, and didin't your teacher explain this?

Answer 2

I had a textbook hmm about 15 years ago when I was in a class.. and Im sure my teacher did

Answer 3

i think n = 5
and p = 9
n+ p = 14

Answer 4

you're correct.. in fact I have the answer, but Im not sure how it was obtained.. I'd like to see how.

Answer 5

well n= 5 gives 5n =25
then 75n = 75 * 5 = 375
and i guessed 9
375 * 9 = 3375 - taking the cubic root of this gives 15.

Answer 6

so basically its taking educated guesses to arrive at the answer?

Answer 7

the second part was a guess - there's probably a more logical way to do this

Answer 8

the first part had to be n = 5 if you want the lowest possible value

Answer 9

This is actually a question on a practice GRE exam.. I can't imagine solving that logically in under 1 minute (about the time you have per question on the quantitative section)
I'll post the exam guide's explanation.. I dont really get it.. But you probably will

Answer 10

Explanation:

The smallest value for n such that 5n is a square is 5.
75np can now be written as 75 x 5 x p.
This gives prime factors.... 3 x 5 x 5 x 5 x p
To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9
n + p = 5 + 9 = 14

Answer 11

yes! - i should have thought of that way- if a number two duplicate primes as factors and three triplicates it is a perfect cube

Answer 12

I'll have to look up perfect cubes and prime factors I guess.. I'm just not getting this one.. Really rusty with my math..

Answer 13

Thanks though

Answer 14

if a number has even quantities of prime factors it is a perfect square so for example to make 2 x 2 x 3 (12) a perfect square you multiply by 3
= 2 x 2 x 3 x 3 = 36

Answer 15

ah... ok.. I get that..