GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Aug 2020, 02:22

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Jul 2009
Posts: 161
Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

15 Mar 2010, 11:12
4
23
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:33) correct 32% (01:39) wrong based on 646 sessions

### HideShow timer Statistics

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
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1705
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

25 Mar 2014, 18:28
24
4
$$\frac{(2^{12} - 2^6)}{(2^6 - 2^3)}$$

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

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

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

##### General Discussion
Intern
Joined: 23 Feb 2010
Posts: 7

### Show Tags

15 Mar 2010, 11:41
1
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: 165

### Show Tags

15 Mar 2010, 12:04
1
2
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: 119
Schools: ISB

### Show Tags

19 Mar 2010, 00:30
1
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
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

23 Feb 2016, 04:13
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
Math Expert
Joined: 02 Aug 2009
Posts: 8795
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

23 Feb 2016, 04:41
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
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 5033
Location: India
GPA: 3.5
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

02 Mar 2017, 06:37
1
1
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) $$2^6 + 2^3$$
_________________
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 )
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11407
Location: United States (CA)
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

06 Mar 2017, 17:03
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

_________________

# Scott Woodbury-Stewart | Founder and CEO | Scott@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Joined: 26 May 2015
Posts: 6
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

02 Aug 2017, 13:11
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: 4009
Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

03 Aug 2017, 08:10
1
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.
_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
Intern
Joined: 26 May 2015
Posts: 6
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

03 Aug 2017, 11:36
Hi genxer123

Yes, easy mistake to avoid. Thank you for your help. I got it.
Non-Human User
Joined: 09 Sep 2013
Posts: 15603
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)  [#permalink]

### Show Tags

30 Aug 2019, 09:18
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] 30 Aug 2019, 09:18