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

It is currently 19 Aug 2019, 22:34

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

Let a be a positive integer. If n is divisible by 2^a and n is also

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57083
Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 23 Jul 2015, 03:00
2
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:49) correct 33% (01:58) wrong based on 201 sessions

HideShow timer Statistics

CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 23 Jul 2015, 04:23
1
2
Bunuel wrote:
Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by

A. 6
B. 3 × 2^a
C. 2 × 3^(2a)
D. 6^a
E. 6^(2a)

Kudos for a correct solution.


Easiest method is to assume a value of a = 1

Given n is divisible by 2^2 ---> n = 2^1*p ---> n =2p

Also, n is also divisible by 3^(2a) ---> n = 3^(2a) * q = 3^2*q = 9q

Lets look at a few numbers that are multiples of both 2 and 9 are 18,36,72....

Thus looking at the options , A-D divide the numbers 18,36,72.... while E (=6^(2) = 36 ) does not divide 18. Thus E is the correct answer.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 23 Jul 2015, 06:12
1
Bunuel wrote:
Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by

A. 6
B. 3 × 2^a
C. 2 × 3^(2a)
D. 6^a
E. 6^(2a)

Kudos for a correct solution.


Let's Find the smallest Positive Value of n

The Smallest Value of a = 1
i.e. The Smallest Value of 2^a = 2^1 = 2
i.e. The Smallest Value of 3^(2a) = 3^2 = 9

i.e. The smallest value of n Must be divisible by 2 and 9 both
i.e. Smallest value of n = 2*9 = 18

A. 6 Definitely Divisor of n
B. 3 × 2^a = 3*2^1 = 6 Definitely Divisor of n
C. 2 × 3^(2a) = 2*3^2 = 18 Definitely Divisor of n
D. 6^a = 6^1 = 6 Definitely Divisor of n
E. 6^(2a) = 6^2 = 36 NOT a Divisor of n for smallest value of n hence CORRECT OPTION

Answer: Option E
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Manager
Manager
User avatar
Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Re: Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 23 Jul 2015, 06:49
1
Bunuel wrote:
Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by

A. 6
B. 3 × 2^a
C. 2 × 3^(2a)
D. 6^a
E. 6^(2a)

Kudos for a correct solution.


Since, n is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1

Only for E, 6^(2a) doesn't satisfy, if a = 1 and n=18, it is not divisible by 6^2 (i.e 36)


Hence answer is E
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57083
Re: Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 26 Jul 2015, 12:10
1
1
Bunuel wrote:
Let a be a positive integer. If n is divisible by 2^a and n is also divisible by 3^(2a), then it is possible that n is NOT divisible by

A. 6
B. 3 × 2^a
C. 2 × 3^(2a)
D. 6^a
E. 6^(2a)

Kudos for a correct solution.


800score Official Solution:

If n is divisible by 2ᵃ and 3²ᵃ then it must be divisible by least common multiple of 2ᵃ and 3²ᵃ which equals 2ᵃ × 3²ᵃ.

Therefore the smallest possible value number n can take is 2ᵃ × 3²ᵃ which is less than answer choice (E), 6²ᵃ = 2²ᵃ × 3²ᵃ. A larger number can not be a divisor of a smaller one so 2ᵃ × 3²ᵃ is NOT divisible by 6²ᵃ. It means, that 6²ᵃ is not necessarily a divisor of n.

The right answer is choice (E).
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 12034
Re: Let a be a positive integer. If n is divisible by 2^a and n is also  [#permalink]

Show Tags

New post 21 Dec 2018, 17:51
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.
_________________
GMAT Club Bot
Re: Let a be a positive integer. If n is divisible by 2^a and n is also   [#permalink] 21 Dec 2018, 17:51
Display posts from previous: Sort by

Let a be a positive integer. If n is divisible by 2^a and n is also

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





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