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:

Same approach : it's better to plug 2 values mentally with the respect of abs always positive (or 0) than to solve the original equation (saving energy... 4 hours is long)

If |d-9| = 2d, then d= [#permalink]
23 Jan 2011, 07:37

2

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

aurobindo wrote:

If |d-9| = 2d, then d= (A) -9 (B) -3 (C) 1 (D) 3 (E) 9

You can approach this problem in several ways. For example: given |d-9| = 2d --> as LHS (|d-9|) is an absolute value then it's non-negative so RHS (2d or simply d) must also be non-negative thus answer choices A and B are out. Next you can quickly substitute the values to see that d=3 satisfies given inequality: |3-9|=|-6|=6=2*3.

Or you can try algebraic approach and expand |d-9| for 2 ranges: If \(0\leq{d}\leq{9}\) then \(-(d-9)=2d\) --> \(d=3\) --> you have an answer D right away; Just to check the second range: If \({d}>9\) then \(d-9=2d\) --> \(d=-9\) --> not a valid solution as \(d\) cannot be negative (also this value is not in the range we are considering).

Re: If |d-9| = 2d, then d= [#permalink]
02 Oct 2013, 00:35

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 |d-9| = 2d, then d= [#permalink]
22 Oct 2014, 10:36

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 |d-9| = 2d, then d= [#permalink]
15 Jan 2015, 21:47

Expert's post

Hi All,

Since the answer choices to this question are NUMBERS, we can use them (along with some Number Property knowledge) to quickly get to the solution by TESTing THE ANSWERS.

We're given |D - 9| = 2D and we're asked to solve for D

Since the "left" side of the equation will end up as either a 0 or a POSITIVE, the "right side" of the equation CAN'T be negative, so we know that D CANNOT be NEGATIVE. Eliminate A and B.

The solution MUST be one of the remaining 3 answers, so we can just TEST them until we find the correct one.

Could D = 1? |1-9| = |-8| = 8 2D = 2(1) = 2 -8 does NOT = 2 Eliminate C.

Could D = 3? |3-9| = |-6| = 6 2(3) = 6 6 DOES = 6 This IS the answer.

If |d-9| = 2d, then d= [#permalink]
07 May 2015, 22:33

Expert's post

Here's a more visual way to think through the given equation |d - 9| = 2d.

|d-9| represents the distance between point d and 9 on the number line. Now, there are only 2 options - either the point d can lie on the LEFT hand side of 9 (At a distance of |d-9| units from 9) or on the RIGHT hand side of 9.

So, let's depict these two cases on the number line.

Case 1: d < 9

In this case, |d - 9| = 9 - d (also written as -(d-9))

So, the given equation becomes:

9 - d = 2d => d = 3

Case 2: d > 9

In this case, |d - 9| = d - 9

So, the given equation becomes:

d - 9 = 2d => d = -9

But this value of d contradicts the condition of Case 2, that d is greater than 9. Therefore, this value of d can be rejected.

So, we get d = 3.

Usually, this visual way of thinking through absolute value expressions helps a lotin situations where you find yourself getting confused about how to open an absolute value expression, what signs to put, what cases to consider etc.

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

I’ll start off with a quote from another blog post I’ve written : “not all great communicators are great leaders, but all great leaders are great communicators.” Being...