• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

GMAT Prpe

This topic has 11 member replies

GMAT Prpe

Post
I dont know what is the component I should be focussing on while doing this problem

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/3^2*2*5

III.y/3*2*5^2

Thanks

_________________
Maxx

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
05 Sep 2007
Posted:
645 messages
Followed by:
5 members
Upvotes:
34
Post
moneyman wrote:
I dont know what is the component I should be focussing on while doing this problem

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/3^2*2*5

III.y/3*2*5^2

Thanks
450 = 2 x 5^2 x 3^2
Now 2 x 5^2 x 3^2 x y = n^3
So at minimum, y = 2^2 x 5 x 3
So y/3*2^2*5 is the minimum value which will always be integer. Got me, Max?

_________________
Correct me If I am wrong


Regards,

Amitava

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts Default Avatar
Joined
03 Mar 2007
Posted:
468 messages
Upvotes:
5
Post
Got it Amitava..But I really could not figure out the approach..now its clear..Thanks

_________________
Maxx

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
06 May 2007
Posted:
789 messages
Followed by:
6 members
Upvotes:
15
Target GMAT Score:
710
Post
i tried to push numbers out for this and wound up with n=10 and y=2.2

when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.


I tried to break this up into primes but then got lost.

can someone explain this to me in baby steps and please give qa. thanks folks!

_________________
Appetite for 700 and I scraped my plate!

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts Default Avatar
Joined
10 Mar 2008
Posted:
72 messages
Upvotes:
25
Test Date:
April 19, 2008
Target GMAT Score:
730
Post
Enginpasa1 wrote:
i tried to push numbers out for this and wound up with n=10 and y=2.2

when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.


I tried to break this up into primes but then got lost.

can someone explain this to me in baby steps and please give qa. thanks folks!
Step by step:

Find the prime factors of 450.
450
->45*10
->9*5*2*5
-->3*3*5*2*5
--->2*3*3*5*5

The question states that 450y = n^3.
Since y and n are both positive integers, this means that 450y must be a perfect cube.

In order for 450y to be a perfect cube, we look at our current prime factors of 450:
(2) (3*3) (5*5)

Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's.

(2) (3*3) (5*5) * y
->(2) (3*3) (5*5) * [(2*2) (3) (5)]
-->(2*2*2) (3*3*3) (5*5*5) = perfect cube

Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5.

We look at our answer choices and plug in for y.

I)
y/3*2^2*5
-> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer)

II)
y/3^2*2*5
-> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer)

III)
y/3*2*5^2
-> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer)

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
06 May 2007
Posted:
789 messages
Followed by:
6 members
Upvotes:
15
Target GMAT Score:
710
Post
Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral?

_________________
Appetite for 700 and I scraped my plate!

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts Default Avatar
Joined
10 Mar 2008
Posted:
72 messages
Upvotes:
25
Test Date:
April 19, 2008
Target GMAT Score:
730
Post
Enginpasa1 wrote:
Is there a way to approach this problem and not go through all of your steps. Can we force a value for y and n and then test each roman numeral?
To me, this approach makes the most sense, and like camitava showed, it is pretty straightforward. I would not go through my step by step method on paper; rather, a lot of it would be mental.

The underlying process is quite simple:
1. Recognize that 450y must be a perfect cube.
2. Break 450 into its prime factors and see what y at minimum must be to create a perfect cube.
3. Glance at I, II, and III to see if this minimum value of y can cancel all the denominator values.

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member Default Avatar
Joined
06 May 2007
Posted:
789 messages
Followed by:
6 members
Upvotes:
15
Target GMAT Score:
710
Post
i guess the answer hinges on seeing that 450y must be a perfect cube. NOw I get it! thanks

_________________
Appetite for 700 and I scraped my plate!

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
10 Apr 2008
Posted:
27 messages
Upvotes:
1
Post
Great solution. Very Happy

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts Default Avatar
Joined
10 Apr 2008
Posted:
93 messages
Upvotes:
20
Test Date:
Soon enough
Post
Enginpasa1 wrote:
i tried to push numbers out for this and wound up with n=10 and y=2.2

when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.


I tried to break this up into primes but then got lost.

can someone explain this to me in baby steps and please give qa. thanks folks!
A quick suggestion Enginpasa:

On the GMAT, more often than not, there is as much information in the options and the other parts of the question as the actual question itself.

The 3 Roman Numeral statements are CLEAR indicators that Prime factorisation is in some way or the other involved.

Any method that takes us away from that will be longer and relatively more cumbersome.

_________________
For love, not money.

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
24 Jul 2009
Posted:
18 messages
Upvotes:
2
Post
Thank you very much

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
24 Jul 2009
Posted:
18 messages
Upvotes:
2
Post
tmmyc wrote:
Enginpasa1 wrote:
i tried to push numbers out for this and wound up with n=10 and y=2.2

when i plugged them into the answer choices not one of the roman numerals gave an integer. So my first answer is none will give an integer.


I tried to break this up into primes but then got lost.

can someone explain this to me in baby steps and please give qa. thanks folks!
Step by step:

Find the prime factors of 450.
450
->45*10
->9*5*2*5
-->3*3*5*2*5
--->2*3*3*5*5

The question states that 450y = n^3.
Since y and n are both positive integers, this means that 450y must be a perfect cube.

In order for 450y to be a perfect cube, we look at our current prime factors of 450:
(2) (3*3) (5*5)

Therefore, in order for 450y to be a perfect cube, we need an additional 5, an additional 3, and two additional 2's.

(2) (3*3) (5*5) * y
->(2) (3*3) (5*5) * [(2*2) (3) (5)]
-->(2*2*2) (3*3*3) (5*5*5) = perfect cube

Thus, at minimum, y must be [(2*2) (3) (5)] or 2^2 * 3 * 5.

We look at our answer choices and plug in for y.

I)
y/3*2^2*5
-> (2^2 * 3 * 5) / 3*2^2*5 = 1 (integer)

II)
y/3^2*2*5
-> (2^2 * 3 * 5) / 3^2*2*5 = 2/3 (not an integer)

III)
y/3*2*5^2
-> (2^2 * 3 * 5) / 3*2*5^2 = 2/5 (not an integer)
thank you very much, I was surfing the web looking for such a good explanation. Good luck
mat

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Top First Responders*

1 GMATGuruNY 57 first replies
2 Jay@ManhattanReview 51 first replies
3 Brent@GMATPrepNow 46 first replies
4 Ian Stewart 23 first replies
5 ceilidh.erickson 12 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

198 posts
2 image description fskilnik@GMATH

GMATH Teacher

150 posts
3 image description Max@Math Revolution

Math Revolution

90 posts
4 image description GMATGuruNY

The Princeton Review Teacher

84 posts
5 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

78 posts
See More Top Beat The GMAT Experts