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

It is currently 16 Dec 2018, 21:08

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • 10 Keys to nail DS and CR questions

     December 17, 2018

     December 17, 2018

     06:00 PM PST

     07:00 PM PST

    Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If t is divisible by 12, what is the least possible integer value of a

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51230
If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 13 Aug 2018, 03:59
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

65% (01:27) correct 35% (01:51) wrong based on 89 sessions

HideShow timer Statistics

Director
Director
User avatar
P
Joined: 18 Jul 2018
Posts: 502
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 13 Aug 2018, 04:46
Since T is divisible by 12. Let's assume T to be 12. Then, \(T^2\) =144.
Then the minimum value for which \(T^2\) is not an integer when divided by \(2^a\) is when a=5.
Hence D is the answer.
_________________

When you want something, the whole universe conspires in helping you achieve it.

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 13 Aug 2018, 05:55
Bunuel wrote:
If t is divisible by 12, what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


Min Value if \(t^2 = 12^2 =2^4*3^2\)

Thus, all values of \(2\) upto \(2^4\) will result in an integer value, hence Answer must be \((D)5\)
_________________

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 )

Director
Director
User avatar
P
Joined: 31 Oct 2013
Posts: 883
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 13 Aug 2018, 13:46
Bunuel wrote:
If t is divisible by 12, what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6



t is divisible by 12. It means that t is a multiple of 12.

Let's assume t is 12.

\(\frac{12^2}{2^a}\)

=\(\frac{3^2 * 2^4}{2^a}\)

= \(3^2 * 2^{(4 - a)}\)

= \(9 * 2^{(4-5)}\)

= \(9 * 2^{(-1)}\)

For negative exponents we get fraction.

So, least possible integer value of a is 5.

The best answer is D.
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Premium Member
If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 13 Aug 2018, 22:36
Bunuel wrote:
If t is divisible by 12, what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


\(12^2=(3*2^2)^2\)=\(3^2*2^4\)

Now, \(\frac{t^2}{2^a}\)=\(\frac{3^2*2^4}{2^a}\)

The given fraction is an integer when a=2,3,4, and 6 among options.

Ans. (D)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 18 Aug 2018, 17:24
Bunuel wrote:
If t is divisible by 12, what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


Since the smallest positive value of t is 12, and since 12 = 2^2 x 3^1, we see that 12^2 = 2^4 x 3^2. This factorization shows us that any power of 2, from 2^1 to 2^4, inclusive, is guaranteed to divide into t^2. Thus, we are sure that when a is 1, 2, 3, or 4, t^2/2^a is an integer.

Therefore, the smallest value of a such that t^2/2^a might not be an integer is 5.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 25 Apr 2018
Posts: 3
Location: India
Schools: Yale '21
GPA: 3.49
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 22 Aug 2018, 09:46
1
Hi, Lets assume t=48 and if we try to solve it, it is divisible by 2^5. Can you please explain why this is happening?
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Premium Member
Re: If t is divisible by 12, what is the least possible integer value of a  [#permalink]

Show Tags

New post 23 Aug 2018, 13:04
1
akankshaboparai wrote:
Hi, Lets assume t=48 and if we try to solve it, it is divisible by 2^5. Can you please explain why this is happening?


Hi akankshaboparai,
Question stem:- what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) MIGHT NOT be an integer?

1) We have been asked to find the least possible integer value of 'a'.
2) As assumed, at t=48 and a=5, the given fraction is an integer. (Correct, but least possible value of 'a' would be obtained when 't' is the minimum. ). Does a=5 produce integer values of the fraction at all 't'? NO (Discard this scenario)
3) Here t=12k, k is a positive integer.
4) So we have to check at t=12*1=12 (At minimum 't')
\(\frac{12^2}{2^a}\)=\(\frac{2^4*3^2}{2^a}\) doesn't yield an integer at a=5 and 6. But it yields integers at a=1,2,3, and 4.

Between 5 and 6, 5 is the least possible value.

Hope it helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

GMAT Club Bot
Re: If t is divisible by 12, what is the least possible integer value of a &nbs [#permalink] 23 Aug 2018, 13:04
Display posts from previous: Sort by

If t is divisible by 12, what is the least possible integer value of a

  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®.