Last visit was: 17 Jul 2025, 15:16 It is currently 17 Jul 2025, 15:16
Close
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
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,280
 [112]
3
Kudos
Add Kudos
109
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,280
 [22]
5
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
User avatar
exc4libur
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,702
Own Kudos:
1,431
 [5]
Given Kudos: 607
Location: United States
Posts: 1,702
Kudos: 1,431
 [5]
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 17 Jul 2025
Posts: 6,377
Own Kudos:
15,602
 [3]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,377
Kudos: 15,602
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D
avatar
Euphor1a
Joined: 05 Sep 2018
Last visit: 23 Nov 2018
Posts: 5
Own Kudos:
Given Kudos: 8
Posts: 5
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATinsight
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D

Hey Insight,

Hope you're well.

In a question like this, why can't I multiply out the brackets to make a quadratic equation then solve for x? For example, once I multiplied and simplified the above, I deduced: x^2 + 4x - 5 = 0, where x = -5 or 1. Therefore, the answer would be -5.

May you point out the flaw in my reasoning please?

Thanks in advance.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 17 Jul 2025
Posts: 6,377
Own Kudos:
15,602
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,377
Kudos: 15,602
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Euphor1a
GMATinsight
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D

Hey Insight,

Hope you're well.

In a question like this, why can't I multiply out the brackets to make a quadratic equation then solve for x? For example, once I multiplied and simplified the above, I deduced: x^2 + 4x - 5 = 0, where x = -5 or 1. Therefore, the answer would be -5.

May you point out the flaw in my reasoning please?

Thanks in advance.

It's not bracket (parenthesis) it's modulus sign which considers absolute value i.e. the part inside may be positive as well as negative. You have skipped the possibility of the x+2 to be negative when you treat it like a bracket.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 17 Jul 2025
Posts: 16,111
Own Kudos:
74,374
 [36]
Given Kudos: 475
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,111
Kudos: 74,374
 [36]
17
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

We always say that you need to keep an eye on the options from the beginning. Here, I see an equation with absolute values and we are looking for its solutions.
The product of the solutions look like easy numbers (I think -4, 5 etc).
I notice 0 and the first thing I do here is check for 0. Does x = 0 work? If yes, the product will be 0 no matter what the other values of x are.
x = 0 works!
We are done.

Answer (D)
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 17 Jul 2025
Posts: 8,350
Own Kudos:
4,830
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,350
Kudos: 4,830
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the product of all possible solutions of the equation |x+2|2−5|x+2|=−6|x+2|2−5|x+2|=−6?

A. -20
B. -5
C. -4
D. 0
E. 20

Let |x+2|= Y
y^2-5y+6=0

solve for y = 2,3

since |x+2|= Y
we get values, 0,1,2,3
product would be 0 hence D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,280
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

User avatar
CEdward
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,212
Own Kudos:
Given Kudos: 332
Posts: 1,212
Kudos: 247
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
Bunuel
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

We always say that you need to keep an eye on the options from the beginning. Here, I see an equation with absolute values and we are looking for its solutions.
The product of the solutions look like easy numbers (I think -4, 5 etc).
I notice 0 and the first thing I do here is check for 0. Does x = 0 work? If yes, the product will be 0 no matter what the other values of x are.
x = 0 works!
We are done.

Answer (D)

So it looks like in this instance if you plug in 0, it works. But doing that presupposes that x = 0. Isn't the question asking what is the product of xy?

Actually...so x = 0 ... xy = 0.
User avatar
Champer21
Joined: 26 Oct 2023
Last visit: 30 Jul 2024
Posts: 7
Own Kudos:
Given Kudos: 128
Location: Germany
Concentration: Real Estate, Finance
Posts: 7
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can somebody please show me how to insert the values of 3 and 2, to get the the four values of x?

I mean this step:


If a=3=|x+2|a=3=|x+2| then x=1or−5x=1or−5

If a=2=|x+2|a=2=|x+2| then x=0or−4
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
742,280
 [1]
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,280
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Champer21
Can somebody please show me how to insert the values of 3 and 2, to get the the four values of x?

I mean this step:


If a=3=|x+2|a=3=|x+2| then x=1or−5x=1or−5

If a=2=|x+2|a=2=|x+2| then x=0or−4

We denoted |x + 2| as a, and then got that a = 3 or a = 2. Hence, |x + 2| = 3 or |x + 2| = 2.

If |x + 2| = 3, then either x + 2 = 3 or x + 2 = -3. Thus, x = 1 or x = -5.
If |x + 2| = 2, then either x + 2 = 2 or x + 2 = -2. Thus, x = 0 or x = -4.

Hope it's clear.
User avatar
Champer21
Joined: 26 Oct 2023
Last visit: 30 Jul 2024
Posts: 7
Own Kudos:
Given Kudos: 128
Location: Germany
Concentration: Real Estate, Finance
Posts: 7
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Champer21
Can somebody please show me how to insert the values of 3 and 2, to get the the four values of x?

I mean this step:


If a=3=|x+2|a=3=|x+2| then x=1or−5x=1or−5

If a=2=|x+2|a=2=|x+2| then x=0or−4

We denoted |x + 2| as a, and then got that a = 3 or a = 2. Hence, |x + 2| = 3 or |x + 2| = 2.

If |x + 2| = 3, then either x + 2 = 3 or x + 2 = -3. Thus, x = 1 or x = -5.
If |x + 2| = 2, then either x + 2 = 2 or x + 2 = -2. Thus, x = 0 or x = -4.

Hope it's clear.

Thank you very much Bunuel. It is not normal how fast you reply.
Only the best for you!
User avatar
unraveled
Joined: 07 Mar 2019
Last visit: 10 Apr 2025
Posts: 2,727
Own Kudos:
Given Kudos: 763
Location: India
WE:Sales (Energy)
Posts: 2,727
Kudos: 2,171
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20

Since its a polynomial of degree two, we will get two answers - unless we have zero. However, it is absolute value that gets two values so any variable inside the absolute would have four values - unless we have zero.

Let's say y = |x+2|
Therefore,
\(y^2 - 5y = -6\)
gives y = 3 and 2

|x+2| = 3 gives x = 1 and -5
|x+2| = 2 gives x = 0

Now, this gives product as zero.

Answer D.
User avatar
Anu2021
Joined: 12 Jun 2021
Last visit: 06 Jul 2025
Posts: 2
Given Kudos: 1
Posts: 2
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is it wrong to treat the absolute value like parentheses?
I considered it as parentheses and got -
x^2 + 4 + 4x -5x - 10 = -6
x^2 -x = 0
x(x-1) = 0

Therefore, x = 1 and x = 0.
On multiplication of the roots 1 and 0 , you get 0.
ans (D).

Is this approach wrong? If yes, why?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,605
Own Kudos:
Given Kudos: 98,220
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,605
Kudos: 742,280
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Anu2021
Is it wrong to treat the absolute value like parentheses?
I considered it as parentheses and got -
x^2 + 4 + 4x -5x - 10 = -6
x^2 -x = 0
x(x-1) = 0

Therefore, x = 1 and x = 0.
On multiplication of the roots 1 and 0 , you get 0.
ans (D).

Is this approach wrong? If yes, why?

Absolute value and parentheses are not the same.

Absolute Value



For more check Ultimate GMAT Quantitative Megathread

Moderators:
Math Expert
102605 posts
PS Forum Moderator
698 posts