integers

Expert replies

daretodream: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Tue Oct 28, 2008 6:08 am; Thanked: 2 times

by daretodream » Fri Feb 19, 2010 3:32 am

If n and y are positive integers, and 450y=n^3 , which of the following is 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

Like this post

Source: Beat The GMAT — Problem Solving | Fri Feb 19, 2010 3:32 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Fri Feb 19, 2010 3:42 am

daretodream wrote:If n and y are positive integers, and 450y=n^3 , which of the following is 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

450 y = n^3

450 = 3*3*5*5*2

in order for 450 to have a cube root we need 3 of each number of 3*3*3*5*5*5*2*2*2

we already have two 3's and two 5's and one 2

therefore we need one 3, one 5, and 2 twos

or 3 x 5 x 2^2

that would give answer I

Like this post

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Fri Feb 19, 2010 4:51 am

thephoenix wrote:
daretodream wrote:If n and y are positive integers, and 450y=n^3 , which of the following is 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
450 y = n^3

450 = 3*3*5*5*2

in order for 450 to have a cube root we need 3 of each number of 3*3*3*5*5*5*2*2*2

we already have two 3's and two 5's and one 2

therefore we need one 3, one 5, and 2 twos

or 3 x 5 x 2^2

that would give answer I

Hey thephoenix,
I think you could have done a mistake over here.
The correct answer is B but in haste you could have chosen the answer as A as in your answer you had written:-

that would give answer I

It is a similar mistake that I did in the probability question and didn't consider the sample space.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

Like this post

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 19, 2010 12:33 pm

daretodream wrote:If n and y are positive integers, and 450y=n^3 , which of the following is 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

450y=n^3
2*3^2*5^2*y = n^3

n^3 has all the prime factors with powers multiples of three

so y should have 2^2*5*3 as factor (at least)

so y / ( 3 * 2^2 * 5 ) is an integer, others may or may not be an integer

B

Always borrow money from a pessimist, he doesn't expect to be paid back.

Like this post

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 6:07 am

daretodream wrote:If n and y are positive integers, and 450y=n^3 , which of the following is 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

450 = 3x3x5x5x2
450 y = n^3 --> n = cube root(450 y)
so for 450 y to be a perfect cube , we need to add more 3, 5 and 2 as a factor 0f y

[spoiler]so y is a multiple of 3x5 x 2^2

so only I i.e. B[/spoiler]

My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.

Like this post

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Feb 20, 2010 8:18 am

thephoenix wrote:
daretodream wrote:If n and y are positive integers, and 450y=n^3 , which of the following is 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
450 y = n^3

450 = 3*3*5*5*2

in order for 450 to have a cube root we need 3 of each number of 3*3*3*5*5*5*2*2*2

we already have two 3's and two 5's and one 2

therefore we need one 3, one 5, and 2 twos

or 3 x 5 x 2^2

that would give answer I

WHICH IS OPTION B

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review