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

 It is currently 27 Aug 2016, 15:36

### 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 |d-9| = 2d, then d=

Author Message
TAGS:

### Hide Tags

Director
Affiliations: FRM Charter holder
Joined: 02 Dec 2006
Posts: 734
Schools: Stanford, Chicago Booth, Babson College
Followers: 13

Kudos [?]: 66 [2] , given: 4

If |d-9| = 2d, then d= [#permalink]

### Show Tags

18 Jan 2007, 07:49
2
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

68% (02:30) correct 32% (00:39) wrong based on 848 sessions

### HideShow timer Statistics

If |d - 9| = 2d, then d=

(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
[Reveal] Spoiler: OA
Manager
Joined: 11 Dec 2006
Posts: 51
Followers: 1

Kudos [?]: 4 [1] , given: 0

### Show Tags

18 Jan 2007, 09:42
1
KUDOS
1
This post was
BOOKMARKED
if d>9, on solving eqn u get d = -9 which is impossible since d>9.
if d<9, on sloving u get d = 3. Hence D is correct answer
Director
Joined: 24 Aug 2006
Posts: 751
Location: Dallas, Texas
Followers: 5

Kudos [?]: 117 [0], given: 0

### Show Tags

18 Jan 2007, 23:54
d has two solutions : d=3 and d=-9
D !
_________________

"Education is what remains when one has forgotten everything he learned in school."

Senior Manager
Joined: 24 Oct 2006
Posts: 339
Followers: 1

Kudos [?]: 24 [2] , given: 0

### Show Tags

19 Jan 2007, 03:31
2
KUDOS
1
This post was
BOOKMARKED
IMO

2d is an absolute value, so d can't be negative.

Out of the +ve nos. d can be only 3
SVP
Joined: 01 May 2006
Posts: 1798
Followers: 9

Kudos [?]: 137 [0], given: 0

### Show Tags

19 Jan 2007, 05:31
Sumithra wrote:
IMO

2d is an absolute value, so d can't be negative.

Out of the +ve nos. d can be only 3

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)
Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 2

Kudos [?]: 131 [11] , given: 3

### Show Tags

10 Sep 2009, 11:40
11
KUDOS
4
This post was
BOOKMARKED
If |d-9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9

now the two eqs are
1) when (d-9) > 0
d-9 = 2d
d = -9

2) when (d-9) < 0
9-d = 2d
d = 3

the two initial solns are d = -9 and 3

but when we substitute d = -9 in original equation we get
|-9-9| = 2 * -9
18 = -18
which is not possible

Hence only solution is d = 3.
Intern
Joined: 10 Jan 2011
Posts: 21
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
Followers: 0

Kudos [?]: 3 [0], given: 0

### Show Tags

23 Jan 2011, 07:51
vsaxenaGMAT wrote:
if d>9, on solving eqn u get d = -9 which is impossible since d>9.
if d<9, on sloving u get d = 3. Hence D is correct answer

GOOD EXPLANATION
_________________

Rahul

Math Expert
Joined: 02 Sep 2009
Posts: 34457
Followers: 6279

Kudos [?]: 79667 [3] , given: 10022

If |d-9| = 2d, then d= [#permalink]

### Show Tags

23 Jan 2011, 08:37
3
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).

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11099
Followers: 511

Kudos [?]: 134 [0], given: 0

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

02 Oct 2013, 01:35
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11099
Followers: 511

Kudos [?]: 134 [0], given: 0

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

22 Oct 2014, 11:36
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.
_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 443
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Followers: 2

Kudos [?]: 92 [0], given: 169

If |d-9| = 2d, then d= [#permalink]

### Show Tags

15 Jan 2015, 08:25
I am having some problems with the range when there is an absolute value. Can I find some good material that explains how we get to the range?

Thank you,
Natalia
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7181
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 312

Kudos [?]: 2125 [0], given: 161

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

15 Jan 2015, 22:47
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

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Senior Manager
Joined: 02 Dec 2014
Posts: 375
Location: Russian Federation
Concentration: General Management, Economics
WE: Sales (Telecommunications)
Followers: 0

Kudos [?]: 66 [0], given: 346

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

02 Mar 2015, 02:26
pacifist85 wrote:
I am having some problems with the range when there is an absolute value. Can I find some good material that explains how we get to the range?

Thank you,
Natalia

Hi Natalia! (Looks like you are Russian=))
I think you can read in Gmat Club Mathbook if you still need this information
_________________

"Are you gangsters?" - "No we are Russians!"

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 350
Followers: 103

Kudos [?]: 810 [0], given: 84

If |d-9| = 2d, then d= [#permalink]

### Show Tags

07 May 2015, 23:33
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 lot in situations where you find yourself getting confused about how to open an absolute value expression, what signs to put, what cases to consider etc.

Hope this helped!

Japinder
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11099
Followers: 511

Kudos [?]: 134 [0], given: 0

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

23 May 2016, 06:56
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.
_________________
Director
Joined: 12 Sep 2015
Posts: 555
Followers: 47

Kudos [?]: 387 [0], given: 13

Re: If |d-9| = 2d, then d= [#permalink]

### Show Tags

26 Aug 2016, 07:34
Top Contributor
aurobindo wrote:
If |d - 9| = 2d, then d=

(A) -9
(B) -3
(C) 1
(D) 3
(E) 9

We have two cases to consider:
d - 9 = 2d and d - 9 = -2d

case a: If d - 9 = 2d, then d = -9
When we check this solution for extraneous roots, we get: |-9 - 9| = (2)(-9)
Simplify to get: |-18| = -18
NO GOOD!
So, d = -9 is NOT a valid solution

case b: If d - 9 = -2d, then d = 3
When we check this solution for extraneous roots, we get: |3 - 9| = (2)(3)
Simplify to get: |-6| = 6
WORKS!
So, d = 3 IS a valid solution.

[Reveal] Spoiler:
D

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Brent also tutors students for the GMAT

Re: If |d-9| = 2d, then d=   [#permalink] 26 Aug 2016, 07:34
Similar topics Replies Last post
Similar
Topics:
2 If y = x^2 + d x + 9 does not cut the x-axis, then which of the follow 7 13 Mar 2016, 09:53
4 C/D = 9.75 When dividing positive integer C by positive 5 05 Aug 2014, 11:31
31 The sum S of the arithmetic sequence a, a+d, a+2d,..., 12 03 Jun 2014, 21:30
8 If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the 5 23 May 2014, 12:38
8 If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 7 07 Dec 2009, 11:57
Display posts from previous: Sort by