Last visit was: 17 Jun 2024, 03:24 It is currently 17 Jun 2024, 03:24
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Director
Joined: 02 Dec 2006
Affiliations: FRM Charter holder
Posts: 562
Own Kudos [?]: 418 [47]
Given Kudos: 4
Concentration: Finance, Entrepreneurship
Schools:Stanford, Chicago Booth, Babson College
Q48  V34 GMAT 2: 740  Q49  V42
GPA: 3.53
Manager
Joined: 27 Oct 2008
Posts: 97
Own Kudos [?]: 299 [25]
Given Kudos: 3
Math Expert
Joined: 02 Sep 2009
Posts: 93718
Own Kudos [?]: 632401 [15]
Given Kudos: 82322
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [4]
Given Kudos: 799
Re: If |d-9| = 2d, then d= [#permalink]
3
Kudos
1
Bookmarks
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.

RELATED VIDEO

General Discussion
Intern
Joined: 11 Dec 2006
Posts: 38
Own Kudos [?]: 19 [3]
Given Kudos: 0
2
Kudos
1
Bookmarks
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
Manager
Joined: 24 Oct 2006
Posts: 169
Own Kudos [?]: 61 [5]
Given Kudos: 0
4
Kudos
1
Bookmarks
IMO

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

Out of the +ve nos. d can be only 3
VP
Joined: 01 May 2006
Posts: 1032
Own Kudos [?]: 252 [0]
Given Kudos: 0
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)
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 392 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
If |d-9| = 2d, then d= [#permalink]
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
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11723 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If |d-9| = 2d, then d= [#permalink]
1
Bookmarks
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

GMAT assassins aren't born, they're made,
Rich
Senior Manager
Joined: 02 Dec 2014
Posts: 304
Own Kudos [?]: 302 [0]
Given Kudos: 353
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE:Sales (Telecommunications)
Re: If |d-9| = 2d, then d= [#permalink]
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3717
Own Kudos [?]: 17147 [3]
Given Kudos: 165
If |d-9| = 2d, then d= [#permalink]
2
Kudos
1
Bookmarks
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
Manager
Joined: 21 Jun 2017
Posts: 60
Own Kudos [?]: 39 [0]
Given Kudos: 3
Re: If |d-9| = 2d, then d= [#permalink]
aurobindo wrote:
If |d - 9| = 2d, then d=

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

First, we know that D has to be a positive, because + x + is always a positive; and the absolute value is always positive. Eliminate A, B
Eliminate 1 because, 8 does not equal 2, eliminate 9 because 0 does not equal 18

Therefore (D) 3 is the answer
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6458 [0]
Given Kudos: 1646
Re: If |d-9| = 2d, then d= [#permalink]
aurobindo wrote:
If |d - 9| = 2d, then d=

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

We can solve the equation, first, when (d - 9) is positive, and second, when (d - 9) is negative.

When (d - 9) is positive:

d - 9 = 2d

-9 = d

Looking at the original equation, we see that if d = -9, then |d - 9| = |-18| = 18, but 2d = 2(-9) = -18. We see that is not possible.

So, let’s now solve the equation when (d - 9) is negative.

-(d - 9) = 2d

-d + 9 = 2d

9 = 3d

3 = d

We see that if d = 3, then |3 - 9| = |-6| = 6 and 2d = 2(3) = 6. Thus, d must be 3.

Manager
Joined: 30 May 2018
Posts: 53
Own Kudos [?]: 44 [1]
Given Kudos: 121
Concentration: General Management, Marketing
GMAT 1: 750 Q49 V45
GPA: 3.45
WE:Other (Retail)
Re: If |d-9| = 2d, then d= [#permalink]
1
Kudos
/d-9/ = will give us one negative and one positive outcome.
D will not take negative as in the equation it equals to a positive 2D , hence D needs a positive value .
Solving the above equation gives answer option D as the only answer.
Manager
Joined: 24 Sep 2019
Posts: 138
Own Kudos [?]: 62 [0]
Given Kudos: 1
Re: If |d-9| = 2d, then d= [#permalink]
given:
|d-9| = 2d,
d - 9 = 2d or d - 9 = -2d
An absolute value cannot be negative, so eliminate A and B.
d - 9 = 2d
-9 = d
No negative values, so solve d - 9 = -2d
-9 = -3d
3 = d
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1787
Own Kudos [?]: 2121 [1]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
If |d-9| = 2d, then d= [#permalink]
1
Kudos
Top Contributor
Given that |d - 9| = 2d and we need to find the value of d

Let's solve this using two methods

Method 1: Substitution

Now LHS (Left Hand Side) = Absolute value of a number => it can never be negative
and RHS (Right Hand Side) = 2d
=> negative values of d cannot satisfy this as LHS will be non-negative and RHS will become negative

So, options A and B are out.
Now, let's substitute the value of d from choices C,D,E and see which one satisfies the equation

(C) 1. Put d=1 in |d - 9| = 2d and see if satisfies or not
=> | -1 -9 | = |-10| = 10 $$\neq$$ 2*-1 = -2 => NOT POSSIBLE

(D) 3. Put d=3 in |d - 9| = 2d and see if satisfies or not
=> | 3 -9 | = |-6| = 6 = 2*3 = 6 => POSSIBLE

(E) 9. Put d=9 in |d - 9| = 2d and see if satisfies or not
=> | 9 -9 | = |0| = 0 $$\neq$$ 2*9 = 18 => NOT POSSIBLE

Method 2: Algebra

|d - 9| = 2d
=> d-9 = 2d or d-9 = -2d
=> 2d-d = -9 or d+2d = 9
=> d = -9 or 3d = 9 or d = $$\frac{9}{3}$$ = 3
=> d = -9 or d = 3

If we substitute these values of d back in |d-9| = 2d then we will see that d=-9 does not satisfy the equation
=> d = 3

Hope it helps!

Watch the following video to learn the Basics of Absolute Values

Tutor
Joined: 16 Oct 2010
Posts: 14966
Own Kudos [?]: 65973 [0]
Given Kudos: 435
Location: Pune, India
Re: If |d-9| = 2d, then d= [#permalink]
aurobindo wrote:
If |d - 9| = 2d, then d=

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

The simplest method would be to plug in the options here.

But if one were to do it algebraically, we would remove the absolute value sign using the definition of absolute value:
|d - 9| = (d - 9) if d >= 9
|d - 9| = - (d - 9) if d < 9

Case 1: d >= 9
(d - 9) = 2d
d = -9
Not valid because d must be >= 9

Case 2: d < 9
-(d - 9) = 2d
d = 3
Valid because here d is less than 9.

Check this post for more on this concept:
https://anaprep.com/algebra-the-why-beh ... questions/
Intern
Joined: 25 Jun 2023
Posts: 24
Own Kudos [?]: 12 [0]
Given Kudos: 3
Location: India
GMAT 1: 690 Q49 V34
GMAT 2: 760 Q50 V42
GRE 1: Q169 V155
GPA: 3.74
Re: If |d-9| = 2d, then d= [#permalink]
d-9 = 2d

Or 9-d =2d

D=-9 or d=3

But d can only be positive

Therefore d =3

Therefore D
Re: If |d-9| = 2d, then d= [#permalink]
Moderator:
Math Expert
93718 posts