BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Variables Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 52
Joined: Sat Aug 14, 2010 9:24 pm

Variables Problem

by vongdn » Wed Oct 06, 2010 7:49 pm
If n and y are positive integers and 450y= n^3, which of the following must be an integer?

I. y / (3 * 2^2 * 5)
II. y / (3^3 * 2 * 5)
III. y / (3 * 2 * 5^2)


ANSWER --> I Only

Not sure why that is the answer though, The only thing I can come up with is that I allows me to take the cube root so that it equals n/90.
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 270
Joined: Wed Apr 07, 2010 9:00 am
Thanked: 24 times
Followed by:2 members

by neerajkumar1_1 » Wed Oct 06, 2010 8:06 pm
given 450 y = n^3 is an integer...

hence y = n^3/ 450 will be an integer...

Also 450 = 3^2 * 5^2 * 2

for the RHS to be an integer... the denominator should cancel out evenly..
lets start with the lowest possible value for n = 3 * 5 * 2

so n^3 = 3^3 * 5^3 * 2^3

therefore y = 3^3 * 5^3 * 2^3/ (3^2 * 5^2 * 2)
= 3 * 5 * 2^2

hence y will always be some multiple of the above value...

statement 1) gives us exactly that... hence the number will always be an integer...
statement 2) has a extra 3^2 in the denominator
statement 3) has a extra 5 in the denominator

1 only will give the soln...

Hope this helps!!!
Top
Post new topic Post Reply
• Page 1 of 1