Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Jul 2016, 17:58
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 52 [2] , given: 0

Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 09 Jan 2013, 09:28
2
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

50% (02:42) correct 50% (01:43) wrong based on 601 sessions

HideShow timer Statistics

Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jan 2013, 05:04, edited 1 time in total.
Renamed the topic and edited the question.
2 KUDOS received
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 169

Kudos [?]: 1144 [2] , given: 62

GMAT ToolKit User Premium Member
Re: Absolute Value PS [#permalink]

Show Tags

New post 09 Jan 2013, 10:33
2
This post received
KUDOS
2
This post was
BOOKMARKED
sambam wrote:
Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105


The \(w=|x|\) implies that we are not bothered about the sign.
The expression can be rewritten as \(x=2^b - (2^{90} + 2^{15})\)

Now pick up the available answer choices.
For b=35,
\(x=2^{35} - (2^{90} + 2^{15})\) or \(x=2^{35} - 2^{90}- 2^{15}\) or \(x= 2^{15} (2^{20} -2^{70} -1)\). Since 1 is too less if compared to other available values, hence we neglect it. Now the expression becomes \(x=2^{15}(2^{20}-2^{70})\) or \(x=2^{15} * 2^{20} * (-2^{50})\)

For b=90,
Same approach is applied and x comes out to be as \(-2^{15}\).

For b=91,
Same approach is applied and x comes out as \(2^{15} * 2^{75}\)

For remaining answer choices, x would be even more.
Hence if b=90, we have the smallest value of \(|w|\).
hence +1B
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

9 KUDOS received
Moderator
Moderator
User avatar
Joined: 10 May 2010
Posts: 823
Followers: 25

Kudos [?]: 385 [9] , given: 192

GMAT ToolKit User Premium Member
Re: Absolute Value PS [#permalink]

Show Tags

New post 09 Jan 2013, 11:07
9
This post received
KUDOS
The expression can be rewritten as \(x=2^b - (2^{90} + 2^{15})\)

\(2^{90} >> 2^{15}\) Hence expression becomes \(x=2^b - (2^{90}) - a small quantity\)

Now we know that unless b = 90, the expression will have something of the order of \(2^{90}\) or even more.

Hence B.
_________________

The question is not can you rise up to iconic! The real question is will you ?

5 KUDOS received
Current Student
User avatar
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 70

Kudos [?]: 667 [5] , given: 183

Re: Absolute Value PS [#permalink]

Show Tags

New post 09 Jan 2013, 12:12
5
This post received
KUDOS
Given, \(x=2^b - (8^{30} + 8^{5})\)
i.e. \(x= 2^b - (2^{90} + 2^{15}) = 2^b - 2^{15}(2^{75} + 1) = 2^b - 2^{15}(2^{75}) = 2^b - 2^{90}\)

PS: note that \((2^{75}+1)\approx{2^{75}}\)

Thus x is minimum when b is 90

Choice (B) is the correct answer!
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE: http://gmatclub.com/forum/vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

1 KUDOS received
Manager
Manager
avatar
Joined: 07 Apr 2012
Posts: 126
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)
Followers: 0

Kudos [?]: 10 [1] , given: 45

Re: Absolute Value PS [#permalink]

Show Tags

New post 29 Aug 2013, 03:28
1
This post received
KUDOS
PraPon wrote:
Given, \(x=2^b - (8^{30} + 8^{5})\)
i.e. \(x= 2^b - (2^{90} + 2^{15}) = 2^b - 2^{15}(2^{75} + 1) = 2^b - 2^{15}(2^{75}) = 2^b - 2^{90}\)

PS: note that \((2^{75}+1)\approx{2^{75}}\)

Thus x is minimum when b is 90

Choice (B) is the correct answer!


Can we afford to ignore 2^15 ?, even when options have more than 90 as answers
Manager
Manager
User avatar
Joined: 16 Jan 2011
Posts: 103
Followers: 11

Kudos [?]: 129 [0], given: 13

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 15 Sep 2013, 04:52
x=2^b-2^90-2^15 --> 2^15*(2^(b-15)-2^75) --> i wanna the result within the braces be 0, hence 2^(b-15)=2^75 --> b=90
3 KUDOS received
Manager
Manager
avatar
Joined: 29 Aug 2013
Posts: 78
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29
GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)
Followers: 0

Kudos [?]: 52 [3] , given: 24

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 16 Sep 2013, 10:42
3
This post received
KUDOS
sambam wrote:
Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105


w = |x| means w will be lowest only when x = 0 since any non zero value for x, w will be positive and hence will be greater than 0

Hence,
2^b = (8^30 + 8^5)
2^b = 8^5(8^25 + 1)
2^b = 2^15 ( 2^75) [Neglecting 1 since 8^25 is much much greater than 1)

Therefore 2^b =2^90

b = 90 ------- (b)

Consider Kudos if it helped :)
Senior Manager
Senior Manager
avatar
Status: Student
Joined: 26 Aug 2013
Posts: 266
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Followers: 2

Kudos [?]: 55 [0], given: 401

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 10 Jan 2014, 03:30
Hi,

this is my process for this one:

2^b – (8^(30) + 8^(5)) ==> 2^b - (2^(90) + 2^(15))

Look at the answer choices. Eliminate all except those that are close to 2^90

You only have B and C: b=90 or 91

Now look again at the question: is says \(w = |x|\). Coincidence? Never!

In fact you can have here a negative number because you have |x|.

Therefore bewteen 2^(15) (in fact it is - 2^(15) but as I said you are dealing with absolute value here so it is 2^(15)) and 2^(91) - 2^90 + 2^(15) which is the smallest?

2^(15) for sure (there is a huge difference here)!

Answer is therefore B.

Hope it helps!
_________________

Think outside the box

Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 125
Followers: 7

Kudos [?]: 82 [0], given: 1

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 10 Jan 2014, 05:06
sambam wrote:
Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105


Backsolving will work wonders here:

If we start with any other number apart from 90

|2^something - 2^90 - 2^15| will always be greater than 2^15

Hence the only way it can be lowest i.e. 2^15 when b = 90 and 2^90 - 2^90 = 0

Hence answer is B
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10619
Followers: 495

Kudos [?]: 130 [0], given: 0

Premium Member
Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 15 May 2015, 10:29
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 29 May 2015
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 4

CAT Tests
Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 23 Sep 2015, 01:04
This is how i thought about the problem.

Whenever i see big numbers such as 8^30, i assume that it should be simplified somehow, as we are not allowed to use calculator.
In thinking so, seeing 2^b is a relief because 8^30 can be written as 2^3^30 = 2^90


So we get, x= 2^b - (2^90 + 2^15)
Afterwards, plug choices.

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105
Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6755
Location: Pune, India
Followers: 1876

Kudos [?]: 11549 [5] , given: 219

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink]

Show Tags

New post 23 Sep 2015, 05:34
5
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
sambam wrote:
Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35
(B) 90
(C) 91
(D) 95
(E) 105



This question has a few noteworthy points.
To get the smallest value of w (which is non negative), 2^b should be as close as possible to \((8^{30} + 8^5)\).

\(8^{30} + 8^5) = (2^{90} + 2^{15})\)

Now a valid question is this: what is closer to \((2^{90} + 2^{15})\): \(2^{90}\) or \(2^{91}\) or higher powers? Let's focus on \(2^{90}\) and \(2^{91}\) only first.

Note a few things: \(2^{91} = 2^{90} * 2^1\)

In other words, it is two times \(2^{90}\) i.e. \(2^{90} + 2^{90}\)

So the question comes down to this: Is \((2^{90} + 2^{15})\) closer to \(2^{90} + 0\) or \(2^{90} + 2^{90}\)

Now, it is obvious that \(2^{15}\) will be much smaller than \(2^{90}\).
\(2^{15}\) is equidistant from 0 and \(2^{16}\) on the number line (because using the same logic, \(2^{16} = 2^{15} + 2^{15}\)).
So \(2^{15}\) will be much closer to 0 compared with \(2^{90}\).

So \((2^{90} + 2^{15})\) is closer to \(2^{90} + 0\) i.e. \(2^{90}\).

Hence, b must be 90.

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the   [#permalink] 23 Sep 2015, 05:34
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If x = -|w|, which of the following must be true nalinnair 7 22 May 2016, 22:21
7 Experts publish their posts in the topic Given that x = 2^b – (8^30 + 16^5), which of the following values for Bunuel 2 29 Feb 2016, 12:55
6 Experts publish their posts in the topic For which of the following functions does f(x) = f(1/x), given that x Bunuel 6 03 Jul 2015, 03:20
5 Experts publish their posts in the topic If x= 2^b - (8^8 + 8^6), for which of the following b values abhisheksharma85 5 20 Sep 2013, 11:12
10 Experts publish their posts in the topic Given that x^4 – 25x^2 = -144, which of the following is NOT subhashghosh 9 30 Jan 2011, 04:38
Display posts from previous: Sort by

Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.