Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 00:18

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x= 2^b - (8^8 + 8^6), for which of the following b values

Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Jun 2013
Posts: 4
Followers: 0

Kudos [?]: 12 [1] , given: 7

If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

20 Sep 2013, 11:12
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:19) correct 41% (01:19) wrong based on 241 sessions

### HideShow timer Statistics

If x= 2^b - (8^8 + 8^6), for which of the following b values is x closest to 0?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Sep 2013, 11:18, edited 1 time in total.
RENAMED THE TOPIC.
Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106067 [1] , given: 11607

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

20 Sep 2013, 11:23
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
abhisheksharma85 wrote:
If x= 2^b - (8^8 + 8^6), for which of the following b values is x closest to 0?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42

$$8^8 + 8^6=8^2*8^6 + 8^6=64*8^6+8^6=65*8^6=65*2^{18}\approx{2^{6}*2^{18}}=2^{24}$$.

$$2^b - (8^8 + 8^6)=0$$ --> $$2^b - 2^{24}=0$$ --> $$b=24$$

OR: 8^8 + 8^6 is very close to 8^8=2^24, thus b=24.
_________________
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4035
Followers: 1416

Kudos [?]: 6764 [0], given: 84

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

20 Sep 2013, 11:27
abhisheksharma85 wrote:
If x= 2^b - (8^8 + 8^6), for which of the following b values is x closest to 0?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42

Dear abhisheksharma85,
I'm happy to help with this.

Recall the exponent rule:
(a^m)^n = a^(m*n)

Therefore,
8^8 + 8^6 = (2^3)^8 + (2^3)^6 = 2^24 + 2^18

This is the thing we want to cancel with 2^b. Well, keep in mind that 2^24 is 2^6 = 64 times larger than 2^18, so for the purposes of cancelling, we will ignore the tinier number. If we want to cancel the 2^24, we need b = 24, answer = (B).

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106067 [1] , given: 11607

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

20 Sep 2013, 11:31
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
abhisheksharma85 wrote:
If x= 2^b - (8^8 + 8^6), for which of the following b values is x closest to 0?

(A) 20
(B) 24
(C) 25
(D) 30
(E) 42

$$8^8 + 8^6=8^2*8^6 + 8^6=64*8^6+8^6=65*8^6=65*2^{18}\approx{2^{6}*2^{18}}=2^{24}$$.

$$2^b - (8^8 + 8^6)=0$$ --> $$2^b - 2^{24}=0$$ --> $$b=24$$

OR: 8^8 + 8^6 is very close to 8^8=2^24, thus b=24.

Similar questions to practice:
the-value-of-10-8-10-2-10-7-10-3-is-closest-to-which-of-95082.html
which-of-the-following-is-closest-to-10180-1030-a-110224.html
which-of-the-following-best-approximates-the-value-of-q-if-99674.html
new-tough-and-tricky-exponents-and-roots-questions-125956-40.html
if-x-10-10-x-2-2x-7-3x-2-10x-2-is-closest-to-143897.html
1-0-0001-0-04-10-the-value-of-the-expression-above-is-59398.html
m24-q-7-explanation-76513.html
10-180-10-30-which-of-the-following-best-approximates-84309.html

Hope it helps.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2168 [0], given: 193

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

26 Feb 2014, 21:08
8^8 = 2^24
8^6 = 2^18

2^24 + 2^18 is nearly to 2^24, so b=24 = Answer = B
_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15434
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

16 Jun 2015, 03:12
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 Legend
Joined: 09 Sep 2013
Posts: 15434
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If x= 2^b - (8^8 + 8^6), for which of the following b values [#permalink]

### Show Tags

02 Dec 2016, 05:54
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: If x= 2^b - (8^8 + 8^6), for which of the following b values   [#permalink] 02 Dec 2016, 05:54
Similar topics Replies Last post
Similar
Topics:
5 If for some value of x, 5^x + 5^(–x) = B, then which of the following 6 26 Feb 2017, 07:42
13 Given that x = 2^b – (8^30 + 16^5), which of the following values for 2 29 Feb 2016, 22:09
4 If x = 8^6 - 5^6, which of the following is NOT a factor of x? 2 27 Nov 2014, 02:52
10 If a^2b > 1 and b < 2, which of the following could be the value of a? 9 19 May 2016, 03:40
31 For which of the following values of x is 16 11 Jun 2016, 10:48
Display posts from previous: Sort by