Last visit was: 17 Jun 2024, 01:19 It is currently 17 Jun 2024, 01:19
Toolkit
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.

# Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 16 Jul 2009
Posts: 140
Own Kudos [?]: 2460 [40]
Given Kudos: 3
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7266 [33]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [4]
Given Kudos: 799
General Discussion
Intern
Joined: 23 Feb 2010
Posts: 4
Own Kudos [?]: 5 [1]
Given Kudos: 6
1
Bookmarks
2^12 = 2^6 * 2^6

1. 2^12 - 2^6 = 2^6 * 2^6 - 2^6 = 2^6 (2^6 -1)
2. 2^6 - 2^3 = 2^3 * 2^3 - 2^3 = 2^3 (2^3 -1)

2^6 / 2^3 = 2^(6-3)=2^3
2^6 -1 = (2^3)^2 – (1)^2 =(2^3 +1) (2^3 – 1) [Hint a^2 - b^2]

Dividing
2^3(2^3 +1) = 2^6 + 2^3

Manager
Joined: 13 Dec 2009
Posts: 112
Own Kudos [?]: 939 [3]
Given Kudos: 13
Concentration: Consulting
Q49  V40
1
Kudos
2
Bookmarks
abhi758 wrote:
Which of the following is equal to $$\frac{2^1^2 - 2^6}{2^6 - 2^3}$$?

A. $$2^6 + 2^3$$
B. $$2^6 - 2^3$$
C. $$2^9$$
D. $$2^3$$
E. 2

Kindly show your working. OA to be posted soon..

(2^12 - 2^6)/(2^6 - 2^3)
= (2^6*(2^6 - 1))/(2^3*(2^3-1))
=2^3 * (2^3+1) * (2^3 - 1) / (2^3 - 1)
=2^3 * (2^3 + 1) = 2^6 + 2^3

Manager
Joined: 18 Feb 2010
Posts: 102
Own Kudos [?]: 641 [1]
Given Kudos: 0
Concentration: Finance
Schools:ISB
Q44  V28 GMAT 2: 620  Q51  V23
1
Kudos
abhi758 wrote:
Which of the following is equal to $$\frac{2^1^2 - 2^6}{2^6 - 2^3}$$?

A. $$2^6 + 2^3$$
B. $$2^6 - 2^3$$
C. $$2^9$$
D. $$2^3$$
E. 2

Kindly show your working. OA to be posted soon..

Using the formula a^2 - b^2 = (a+b) (a-b) we can easily get the answer as A
Intern
Joined: 28 Oct 2015
Posts: 21
Own Kudos [?]: 23 [0]
Given Kudos: 218
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
I did it a slightly different. and I was unable identify the solution. But the answer is correct.

2^6(2^6-1)/2^3(2^3-1)= 2^3*9= 72. Which is equal ro 2^6+2^3
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11443
Own Kudos [?]: 33518 [0]
Given Kudos: 317
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
I did it a slightly different. and I was unable identify the solution. But the answer is correct.

2^6(2^6-1)/2^3(2^3-1)= 2^3*9= 72. Which is equal ro 2^6+2^3

it is good that you have done it by a different method..
But the best is to use a^2-b^2 formula whenever you see a Q in that format..

$$\frac{(2^{12} - 2^6)}{(2^6 - 2^3)}$$....

= $$\frac{(2^6 + 2^3)(2^6 - 2^3)}{(2^6 - 2^3)}$$....

= $$2^6 + 2^3$$
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6064
Own Kudos [?]: 4744 [4]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
1
Kudos
3
Bookmarks
abhi758 wrote:
Which of the following is equal to $$\frac{2^{12} - 2^6}{2^6 - 2^3}$$?

A. $$2^6 + 2^3$$
B. $$2^6 - 2^3$$
C. $$2^9$$
D. $$2^3$$
E. 2

$$\frac{2^{12} - 2^6}{2^6 - 2^3}$$

$$= \frac{2^6 ( 2^6 - 1 )}{2^3 ( 2^3 - 1 )}$$

$$= \frac{2^3( 2^6 - 1 )}{( 2^3 - 1 )}$$

$$= \frac{2^3( 2^3 - 1 )( 2^3 + 1 )}{( 2^3 - 1 )}$$

$$= 2^3( 2^3 + 1 )$$

$$= 2^6 + 2^3$$

Thus, answer must be (A) $$2^6 + 2^3$$
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19019
Own Kudos [?]: 22420 [0]
Given Kudos: 286
Location: United States (CA)
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
abhi758 wrote:
Which of the following is equal to $$\frac{2^{12} - 2^6}{2^6 - 2^3}$$?

A. $$2^6 + 2^3$$
B. $$2^6 - 2^3$$
C. $$2^9$$
D. $$2^3$$
E. 2

Notice that the numerator is a difference of two squares, so let’s simplify the given expression:

(2^12 - 2^6)/(2^6 - 2^3)

(2^6 + 2^3)(2^6 - 2^3)/(2^6 - 2^3)

2^6 + 2^3

Intern
Joined: 26 May 2015
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 9
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
Hi,

Could someone tell me! what is wrong with my approach. I did that:

( 2^12 - 2^6 ) / ( 2^6 - 2^3 ) =
2^6 ( 2^2 - 1 ) / 2^3( 2^2 - 1 ) =
2^6 / 2^3 =
2^3
Senior SC Moderator
Joined: 22 May 2016
Posts: 5329
Own Kudos [?]: 35661 [1]
Given Kudos: 9464
Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
1
Kudos
Esguitar wrote:
Hi,

Could someone tell me! what is wrong with my approach. I did that:

( 2^12 - 2^6 ) / ( 2^6 - 2^3 ) =
2^6 ( 2^2 - 1 ) / 2^3( 2^2 - 1 ) =
2^6 / 2^3 =
2^3

Esguitar ,when you factored out $$2^6$$ and $$2^3$$, you divided the exponents instead of subtracting them. Easy mistake to make.

$$\frac{a^{12}}{a^{6}} = a^{12-6} = a^{6}$$, and

$$\frac{2^{12}}{2^{6}} = 2^{12-6} = 2^{6}$$

So first factoring would be $$2^{6}(2^{6} - 1)$$

$$2^{12}$$ = 4,096
$$2^6$$ = 64
$$2^2$$ = 4

64*4= 256, not 4,096

Hope it helps.
Intern
Joined: 26 May 2015
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 9
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
Hi genxer123

Yes, easy mistake to avoid. Thank you for your help. I got it.
Non-Human User
Joined: 09 Sep 2013
Posts: 33616
Own Kudos [?]: 838 [0]
Given Kudos: 0
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
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: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]
Moderator:
Math Expert
93696 posts