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

It is currently 20 Oct 2018, 18:45

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If x^2 is divisible by 216, what is the smallest possible value for

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

Hide Tags

Manager
Manager
User avatar
Joined: 28 May 2009
Posts: 148
Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
GMAT ToolKit User
If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 23 Jun 2009, 19:35
1
5
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:10) correct 0% (00:00) wrong based on 91 sessions

HideShow timer Statistics

If x^2 is divisible by 216, what is the smallest possible value for positive integer x?
_________________

New to GMAT Club? Start here

Kindle Flashcards - Quant (Official Gmat Club, miguemick's Quant topics), and Verbal (Official Gmat Club) - in Kindle (azw3) format

Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 25 Aug 2009
Posts: 133
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Re: Smallest possible value of x  [#permalink]

Show Tags

New post 26 Oct 2009, 12:42
4
1
216 = 6^3

if we multiply this by 6 we get 6^4 which can be split into a perfect square = 36^2.
hence the answer is 36.
_________________

Rock On

General Discussion
Manager
Manager
avatar
Joined: 30 May 2009
Posts: 196
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 23 Jun 2009, 19:58
2
I think the answer x=36.

216 = 6X6X6

Now we are asked what is the smallest x such that \(x^2\) is divisible by 216.
To make 6X6X6 a perfect square, we need one more 6.

Hence 6X6X6X6 = \(36^2\) is the smallest \(x^2\) divisible by 216.

What is the OA?
Manager
Manager
User avatar
Joined: 28 May 2009
Posts: 148
Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 24 Jun 2009, 08:45
sdrandom1 wrote:
I think the answer x=36.

216 = 6X6X6

Now we are asked what is the smallest x such that \(x^2\) is divisible by 216.
To make 6X6X6 a perfect square, we need one more 6.

Hence 6X6X6X6 = \(36^2\) is the smallest \(x^2\) divisible by 216.

What is the OA?


This is correct the OA is 36.

I like your reasoning better than the Guides

Guides explanation
Quote:
The prime box of \(x^2\)contains the prime factors of 216, which are 2, 2, 2, 3, 3, and 3. We know that the prime factors of \(x^2\) should be the prime factors of x appearing in sets of two, or pairs. Therefore, we should distribute the prime factors of \(x^2\) into two columns to represent the prime factors of x. We see a complete pair of two 2's in the prime box of \(x^2\), so x must have a factor of 2. However, there is a third 2 left over. That additional factor of 2 must be from x as well, so we assign it to one of the component x columns. Also, we see a complete pair of two 3's in the prime box of \(x^2\), so x must have a factor of 3. However, there is a third 3 left over. That additional factor of 3 must be from x as well, so we assign it to one of the component x columns. Thus, x has 2, 3, 2, and 3 in its prime box, so x must be a positive multiple of 36.

_________________

New to GMAT Club? Start here

Kindle Flashcards - Quant (Official Gmat Club, miguemick's Quant topics), and Verbal (Official Gmat Club) - in Kindle (azw3) format

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 265
Re: Smallest possible value of x  [#permalink]

Show Tags

New post 26 Oct 2009, 13:41
2
Yep, Atish is right, I got 36 too

I almost did the same thing as Atish, except I further split 216 into\(2^3*3^3\) and for it be a perfect square we need 2*3
so \(2^2*3^2\) = 36 is the answer
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Director
Director
User avatar
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 801
Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 13 Feb 2011, 11:20
1
216 = 2^3 x 3^3

now, (x^2)/216 is an integer

So x must have atles 3 twos and 3 threes

to make it a perfect square, we multiply x^2 with one more 2 and one more 3...

x^2 = 2^3 x 3^3 x 2 x 3 = 2^4 x 3^4

x = sq. rt.(2^4 x 3^4)
x = 2^2 x 3^2
x = 4 x 9
x = 36
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 14 Mar 2016, 01:07
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 14 Mar 2016, 03:28
Chiragjordan wrote:
I cannot find the options..
Please add the Options along with OA
Also without looking at the options
as 2,3 are prime factors of x and x^2 is divisible by 216
so x must be at least => 36


No options were provided for this question in the source.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 22 Apr 2016, 10:12
There are Three ways we can solve this question
The Easiest way => track the values i.e. using options start with the smallest value and check if it is divisible by 216 or not . P.S => Choose the least value.
The easier way => x is an integer => x^2 will be perfect square => x=36
Slightly complicated way => x and x^2 have same Prime factors . now x^2 must have 2 and 3 as its prime factors so x= 2*3*p where p is some number
Now x^2 = 36p^2 .
but x^2 is divisible by 216
so p=6 atleast
hence x=36 is the least value of x
_________________


MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Manager
Manager
User avatar
B
Joined: 20 Jan 2017
Posts: 60
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Reviews Badge
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 24 Jan 2017, 19:18
1) 216 consists of the following prime factors 2*2*2*3*3*3
2) x should have at least two 2's and two 3's as prime factors in order for its square to be divisible by 216.
3) x=2*2*3*3=36
Intern
Intern
avatar
B
Joined: 24 Jan 2017
Posts: 17
If x2 is divisible by 216, what is the smallest possible value for...  [#permalink]

Show Tags

New post 29 Mar 2017, 15:05
If x2 is divisible by 216, what is the smallest possible value for positive integer x?

I came across this problem in one of my study guides. I still don't understand how to do the work even with the explanation provided.

Can someone explain how to tackle this problem?

Thanks in advance.
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4493
If x2 is divisible by 216, what is the smallest possible value for...  [#permalink]

Show Tags

New post 29 Mar 2017, 16:11
1
Equinocs wrote:
If x2 is divisible by 216, what is the smallest possible value for positive integer x?

I came across this problem in one of my study guides. I still don't understand how to do the work even with the explanation provided.

Can someone explain how to tackle this problem?

Thanks in advance.

Dear Equinocs,

I'm happy to respond. :-)

First of all, if please use proper math notation. For x-squared, you can write x^2 or \(x^2\) using the math notation function. Please do not write x2, because this will generate tremendous confusion.

If you happen to know the cubes of all the single digit numbers, that would be easier, because \(6^3 = 216\). I think all students should have those ten cubes memorized, but let's assume that you didn't know that.

A HUGE help in all kinds of questions about factors and divisible and so forth is the idea of prime factorization. See:
GMAT Math: Factors

Let's start simply by breaking up 216 into factors.
216 = 2*108 = 2*2*54
= 2*2*6*9
= 2*2*2*3*3*3

That's the prime factorization of 216. Whenever you have a particular big number in a question about find the factors or multiples etc, chances are very good that finding the prime factorization of the big number given will be helpful.

Now, another big idea about factors. When we square a number, the factors are doubled: for each single factor, we get a pair of those factors.
\(35 = 5*7\)
\(35^2 = 5*5*7*7\)

\(18 = 2*2*3\)
\(18^2 = 2*2*2*2*3*3\)

Now, let's go back and look at the prime factorization of 216. We can group some of the factors into pairs.
216 = (2*2)*(3*3)*2*3
We have paired and unpaired factors, so to turn this into a perfect square, we would have to multiply by another 2 and another 3, so those factors are paired up.
x^2 = (2*2)*(3*3)*(2*2)*(3*3)
When we take a square-root, each pair of factors becomes a single factor.
x = 2*3*2*3 = 36

Thus, x = 36.

Does this make more sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Intern
Intern
avatar
B
Joined: 24 Jan 2017
Posts: 17
Re: If x2 is divisible by 216, what is the smallest possible value for...  [#permalink]

Show Tags

New post 29 Mar 2017, 16:31
Awesome!

Thank you so much! My apologies for the x2 (x^2).
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: If x^2 is divisible by 216, what is the smallest possible value for  [#permalink]

Show Tags

New post 29 Mar 2017, 21:30
Equinocs wrote:
If x2 is divisible by 216, what is the smallest possible value for positive integer x?

I came across this problem in one of my study guides. I still don't understand how to do the work even with the explanation provided.

Can someone explain how to tackle this problem?

Thanks in advance.


Merging topics. Please refer to the discussion above.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: If x^2 is divisible by 216, what is the smallest possible value for &nbs [#permalink] 29 Mar 2017, 21:30
Display posts from previous: Sort by

If x^2 is divisible by 216, what is the smallest possible value for

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.