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

Redeem

n & y are positive integers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Thu Oct 08, 2009 12:34 am

n & y are positive integers

by GhassanMBA » Fri Feb 12, 2010 11:03 am
Hello everyone this is a question I encountered as i was going through GMAT Prep 1:

If n and y are positive integers and 450 * y = n^3, which of the following must be an integer?

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

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

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

A) None
B) I only
C) II only
D) III only
E) I, II, and III


The OA is B

Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 184
Joined: Sat Apr 14, 2007 9:23 am
Location: Madison, WI
Thanked: 17 times

by ldoolitt » Fri Feb 12, 2010 12:38 pm
GhassanMBA wrote:Hello everyone this is a question I encountered as i was going through GMAT Prep 1:

If n and y are positive integers and 450 * y = n^3, which of the following must be an integer?

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

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

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

A) None
B) I only
C) II only
D) III only
E) I, II, and III


The OA is B

Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks
Anything with integers, divisors, etc you can recognize as a factoring problem. Factor out 450 into its prime factors:

450 -> 2,3,3,5,5

n^3 must have ATLEAST these prime factors for the equality to be true. Note the pattern: you have one 2, two 3s and two 5s. What prime factors COULD n have that would make this relatively close? 2, 3 and 5 naturally!

n -> 2,3,5

looking at the factors...

(2,3,3,5,5) * (?) = (2,3,5) * (2,3,5) * (2,3,5) = (2,2,2,3,3,3,5,5,5)

therefore the prime factors of y must be AT MINIMUM

(2,2,3,5)

Therefore y will be divisible by 2*2*3*5. Choose (b)
Top
User avatar
MBA Student
Posts: 403
Joined: Tue Dec 22, 2009 7:32 pm
Thanked: 98 times
Followed by:22 members

by fibbonnaci » Fri Feb 12, 2010 9:10 pm
GhassanMBA wrote: Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks
Gmat prep does not give explanations. It only shows the correct and incorrect answers that you marked. To learn the explanations, you need to look into forums or external sources.
However, almost all the gmat prep questions have been discussed in BTG. you can use the search option in the forum to locate your question.
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Sat Feb 13, 2010 1:33 am
GhassanMBA wrote:Hello everyone this is a question I encountered as i was going through GMAT Prep 1:

If n and y are positive integers and 450 * y = n^3, which of the following must be an integer?

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

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

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

A) None
B) I only
C) II only
D) III only
E) I, II, and III


The OA is B

Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks
Given is 2*3*3*5*5*y = n^3 and that y and n are positive integers. The least supply that makes 2*3*3*5*5*y a perfect cube of some positive integer, is 2*2*3*5 = 60, such that n^3 = (2*3*5) ^3 or the least n is 30 and the least y is 60.

I. 3 * 2^2 * 5 = 60, which is a definite multiple of y. So, it's ok

II. 3^2 * 2 * 5 = 90, which is NOT a definite multiple of y. So, it's out

III. Not sure whether it's typo or what, either way 3 2 * 5^2 (taken as 150 or 225 or 800) is NOT a definite multiple of y. So, it's out too

Hence, [spoiler]I only[/spoiler]

[spoiler]B[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Post new topic Post Reply
• Page 1 of 1