GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 15:45 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x and y are positive integers and 4500x = y^3, what is the minimum

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58396
If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 82% (01:16) correct 18% (01:39) wrong based on 111 sessions

HideShow timer Statistics

If x and y are positive integers and 4500x = y^3, what is the minimum possible value of x?

A. 5
B. 6
C. 12
D. 30
E. 90

_________________
Senior Manager  S
Joined: 24 Oct 2016
Posts: 251
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28 GPA: 3.96
WE: Human Resources (Retail Banking)
Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

minimum value for x should be 2*3 hence ans is B
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4777
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

Bunuel wrote:
If x and y are positive integers and 4500x = y^3, what is the minimum possible value of x?

A. 5
B. 6
C. 12
D. 30
E. 90

$$4500x = y^3$$

Or, 2^2 * 3^2 * 5^3 * x = y^3

So, The minimum value of x must be 2*3 = 6

Answer will be (B) 6..

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Senior Manager  Joined: 06 Jun 2016
Posts: 254
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23 GMAT 2: 680 Q49 V34 GPA: 3.9
Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

Bunuel wrote:
If x and y are positive integers and 4500x = y^3, what is the minimum possible value of x?

A. 5
B. 6
C. 12
D. 30
E. 90

4500= (2^2)*(3^2)*(5^3)
4500x= y^3 ==> x=2*3=6
B
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

Bunuel wrote:
If x and y are positive integers and 4500x = y^3, what is the minimum possible value of x?

A. 5
B. 6
C. 12
D. 30
E. 90

We are given that 4500x = y^3, which means that 4500x is a perfect cube. We must remember that all perfect cubes break down to unique prime factors, each of which has an exponent that is a multiple of 3. So, let’s break down 4500 into its prime factors to determine the minimum value of x.

4500 = 45 x 100 = 5 x 9 x 10 x 10 = 5 x 3 x 3 x 2 x 5 x 2 x 5 = 2^2 x 3^2 x 5^3

In order to make 4500x a perfect cube, the smallest value of x is 2^1 x 3^1, so that 4500x = (2^2 x 3^2 x 5^3) x (2^1 x 3^1) = 2^3 x 3^3 x 5^3, which is a perfect cube.

Thus, x = 2^1 x 3^1 = 6.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  S
Joined: 05 Dec 2016
Posts: 236
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29 Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

To answer the question correctly it is needed to understand that if y^3=4500x, than root extraction is possible from 4500x.the
First, we need to do prime factorization of 4500, to discover prime factors and its powers.
So, prime factorization of 4500 = 2^2 * 3^2 * 5^3.
5^3 can be easily extracted from the root, but we still have 2^2 and 3^2, it is obvioud that in order to make it possible to extract from root^3 we need to add 1 power to each of factors 3 & 2, after addition of 3^1*2^1, root^3 extraction has become possible. 3*2 = 6, thus correct answer is B
Non-Human User Joined: 09 Sep 2013
Posts: 13382
Re: If x and y are positive integers and 4500x = y^3, what is the minimum  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If x and y are positive integers and 4500x = y^3, what is the minimum   [#permalink] 21 Oct 2018, 22:49
Display posts from previous: Sort by

If x and y are positive integers and 4500x = y^3, what is the minimum

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  