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

It is currently 21 Sep 2018, 02:59

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 (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)

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

Hide Tags

Manager
Manager
avatar
Joined: 28 Oct 2009
Posts: 84
If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post Updated on: 18 Jun 2018, 04:31
3
7
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:15) correct 23% (01:37) wrong based on 483 sessions

HideShow timer Statistics

If \((2^x)(3^y) = 288\), where x and y are positive integers, then \((2^{x-1})(3^{y-2})\) equals:

A. 16
B. 24
C. 48
D. 96
E. 144

Originally posted by marcusaurelius on 21 May 2010, 11:33.
Last edited by Bunuel on 18 Jun 2018, 04:31, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 08 May 2010
Posts: 132
GMAT ToolKit User
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 21 May 2010, 11:51
4
1
If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)(3^y-2) equals:

16
24
48
96
144


So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=5, y=2. now quickly 2^4(3^0)=16. Than answer should be number 1.

If my comments were helpful to you, please give kudos.
Thanks,
Skip
General Discussion
Manager
Manager
avatar
Joined: 28 Oct 2009
Posts: 84
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 21 May 2010, 11:54
Thanks, I didn't even think to use the prime factorization.
Manager
Manager
avatar
Joined: 07 Oct 2006
Posts: 63
Location: India
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 15 Jun 2010, 04:37
2
Algebraically we can approach the problem in another way as well.

If (2^x)(3^y) = 288
then (2^x-1)(3^y-2) = 288/(2[*]3[*]3)
The reason being the exponent of 2 is reduced by 1 and exponent of 3 is reduced by 2.
Hence, the answer would be 288/18 = 16.

-----------------------------------------------------
Please give kudos, if my comments were helpful.
Intern
Intern
avatar
Joined: 12 Nov 2011
Posts: 1
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 12 Nov 2011, 18:45
skipjames wrote:
If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)(3^y-2) equals:

16
24
48
96
144


So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=5, y=2. now quickly 2^4(3^0)=16. Than answer should be number 1.

If my comments were helpful to you, please give kudos.
Thanks,
Skip


Hi Skip, could you please explain prime factorization and how you count the three's. I think I see how you count the two's by taking 2, 8, and 8 seperately and see how many two's making up each number but I don't quite understand how you get the three's.

Thanks, Steven
Manager
Manager
avatar
Joined: 29 Oct 2011
Posts: 159
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 14 Nov 2011, 14:06
Here's how I do prime factorization.

In one row you start with your number to be factored and in the other column you write the smallest possible prime that number is divisible by. Then you do the same for the (number/prime) and so on until you get to 1.

For example:

number:______288______144______72______36______18______9______3______1 (done)
prime factor:_______2_________2______ 2_______2_______2______3______3

In this case you it's easy to see that 288 = 2*2*2*2*2*3*3 = 2^5 * 3^2.
Manager
Manager
avatar
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 197
Location: Kuwait
Schools: Columbia university
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 15 Nov 2011, 09:27
I approached it by using prime factorization. you need to know how many two's and three's are there in 288. using prime factorization, i got 4 two's and 2 three's.
you just need to plug in the values for x and y and solve the given equation.
(2^5-1)(3^2-2)= (2^4)(3^0)= (16)(1)= 16

hope that helps
_________________

Sky is the limit

Manager
Manager
User avatar
S
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 138
Location: Hungary
Concentration: Accounting, Leadership
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
GMAT ToolKit User
Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)  [#permalink]

Show Tags

New post 29 Apr 2017, 04:25
Prime factorize 288 then do your magic:

\(\left( { 2 }^{ x } \right) \left( 3^{ y } \right) =288\\ \left( { 2 }^{ x } \right) \left( 3^{ y } \right) ={ 2 }^{ 5 }{ 3 }^{ 2 }\\ x=5\\ y=2\\ \\ \left( { 2 }^{ x-1 } \right) \left( { 3 }^{ y-2 } \right) =\left( { 2 }^{ 5-1 } \right) \left( { 3 }^{ 2-2 } \right) ={ 2 }^{ 4 }{ 3 }^{ 0 }=16\)
_________________

"When the going gets tough, the tough gets going!"

|Welcoming tips/suggestions/advices (you name it) to help me achieve a 600|

Re: If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1) &nbs [#permalink] 29 Apr 2017, 04:25
Display posts from previous: Sort by

If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)

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

Events & Promotions

PREV
NEXT


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®.