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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Absolute Value PS [#permalink]
09 Jan 2013, 09:33

2

This post received KUDOS

Expert's post

1

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 _________________

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)!

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...