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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # 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 Manager Joined: 18 Oct 2011 Posts: 87 Location: United States Concentration: Entrepreneurship, Marketing GMAT Date: 01-30-2013 GPA: 3.3 Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink] ### Show Tags Updated on: 10 Jan 2013, 04:04 4 26 00:00 Difficulty: 95% (hard) Question Stats: 51% (02:20) correct 49% (02:23) wrong based on 782 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 Originally posted by sambam on 09 Jan 2013, 08:28. Last edited by Bunuel on 10 Jan 2013, 04:04, edited 1 time in total. Renamed the topic and edited the question. ##### Most Helpful Expert Reply Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8527 Location: Pune, India Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the [#permalink] ### Show Tags 23 Sep 2015, 04:34 5 3 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 Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > GMAT self-study has never been more personalized or more fun. Try ORION Free! ##### Most Helpful Community Reply Retired Moderator Joined: 10 May 2010 Posts: 811 Re: Absolute Value PS [#permalink] ### Show Tags 09 Jan 2013, 10:07 9 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 ? ##### General Discussion VP Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1159 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Re: Absolute Value PS [#permalink] ### Show Tags 09 Jan 2013, 09:33 4 2 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 _________________ Senior Manager Joined: 27 Jun 2012 Posts: 375 Concentration: Strategy, Finance Schools: Haas EWMBA '17 Re: Absolute Value PS [#permalink] ### Show Tags 09 Jan 2013, 11:12 7 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 GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here

Manager
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Re: Absolute Value PS  [#permalink]

### Show Tags

29 Aug 2013, 02:28
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
Joined: 15 Jan 2011
Posts: 101
Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the  [#permalink]

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15 Sep 2013, 03:52
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
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Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the  [#permalink]

### Show Tags

16 Sep 2013, 09:42
5
1
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
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Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the  [#permalink]

### Show Tags

10 Jan 2014, 02:30
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!
_________________

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

### Show Tags

10 Jan 2014, 04:06
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
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Joined: 29 May 2015
Posts: 10
Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the  [#permalink]

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23 Sep 2015, 00:04
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
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Posts: 8757
Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the  [#permalink]

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05 Dec 2017, 04:29
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Re: Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the &nbs [#permalink] 05 Dec 2017, 04:29
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