Since X<0,
-X = +ve X
or
-X = |X|
so you actually get |X| as the answer on solving the eq.
Since X<0 the final answer will be -ve of X or -X
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
sqrroot negative number x absolute value
Source: Beat The GMAT — Problem Solving |
Lets take an example which will make it easier to understand.
Since x<0, let x = -2
So -(x) = - (-2) = 2
Also |x| = |-2| = 2
therefore, -x * |x| = 4
And sqrt(4) = 2
Hence answer will be : 2 = - (-2) = -x
Since x<0, let x = -2
So -(x) = - (-2) = 2
Also |x| = |-2| = 2
therefore, -x * |x| = 4
And sqrt(4) = 2
Hence answer will be : 2 = - (-2) = -x
Hi,Motherjane wrote:Lets take an example which will make it easier to understand.
Since x<0, let x = -2
So -(x) = - (-2) = 2
Also |x| = |-2| = 2
therefore, -x * |x| = 4
And sqrt(4) = 2
Hence answer will be : 2 = - (-2) = -x
I dint quite understand the last line.
Hence answer will be : 2 = - (-2) = -x
Can u explain why it should be -x vs x.
thanks
-Vittal
this is soo confusing
why is the square root of a negative number possible?
or is it square root of a positive number (if so where does the negative come from?)
why is the square root of a negative number possible?
or is it square root of a positive number (if so where does the negative come from?)
Let me try to add some clarity here:jopup wrote:this is soo confusing
why is the square root of a negative number possible?
or is it square root of a positive number (if so where does the negative come from?)
Firstly you are not taking the square root of a negative number.
The question stem tells you that x < 0. In other words, x is a negative number.
So lets take a look at the expression under the sq root sign: "-x|x|"
Keep in mind that x is a negative number, as stated in the question x<0.
-(-x) = x
|-x| = x
So under the sq root, we can simplify the expression as x*x or x^2.
So the sq root of x^2 = x.
Note the following rule: a radical (root) sign in the GMAT, denotes only the non-negative root of a number.
For example sq root of 4 is 2 and -2. However, in the GMAT the answer here should be 2, not -2.
So in our case the sq root of x^2 = x. Since the question tells us that x<0, then this means that the answer is -x.
Hopefully this makes sense.
Hi Vittal,vittalgmat wrote:Hi,Motherjane wrote:Lets take an example which will make it easier to understand.
Since x<0, let x = -2
So -(x) = - (-2) = 2
Also |x| = |-2| = 2
therefore, -x * |x| = 4
And sqrt(4) = 2
Hence answer will be : 2 = - (-2) = -x
I dint quite understand the last line.
Hence answer will be : 2 = - (-2) = -x
Can u explain why it should be -x vs x.
thanks
-Vittal
Let me explain what I meant. You agree with me that the answer is 2.
Now 2 can also be written as - (-2). As negative * negative is positive.
In the example, we have already taken x=-2.
Hence replacing the same above will be : - (x) where x = -2
So the answer is -x.
Hope this clears your doubt.
QUestions I was not able to solve.Please find time to solve and respond:
1: For every positive integer n h(n) is product of all even interegrs 2 to n inclusive.If P is the smallest prime factor of h(100)+1 , then p lies between:
Options are:
A: Between 2 and 10
B:Between 10 and 20
C:Between 20 and 30
D:Between 30 and 40
E: greater than 40
2:Alice's take home pay last year was the same each month and she saved the same fraction of her take home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did save each month.
Answer options:
A 1/2
B 1/3
C 1/4
D 1/5
E 1/6
1: For every positive integer n h(n) is product of all even interegrs 2 to n inclusive.If P is the smallest prime factor of h(100)+1 , then p lies between:
Options are:
A: Between 2 and 10
B:Between 10 and 20
C:Between 20 and 30
D:Between 30 and 40
E: greater than 40
2:Alice's take home pay last year was the same each month and she saved the same fraction of her take home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did save each month.
Answer options:
A 1/2
B 1/3
C 1/4
D 1/5
E 1/6
-
AleksandrM
- Legendary Member
- Posts: 566
- Location: Philadelphia
- Thanked: 31 times
- GMAT Score:640
bluefalcon_7691 wrote:QUestions I was not able to solve.Please find time to solve and respond:
1: For every positive integer n h(n) is product of all even interegrs 2 to n inclusive.If P is the smallest prime factor of h(100)+1 , then p lies between:
Options are:
A: Between 2 and 10
B:Between 10 and 20
C:Between 20 and 30
D:Between 30 and 40
E: greater than 40
2:Alice's take home pay last year was the same each month and she saved the same fraction of her take home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did save each month.
Answer options:
A 1/2
B 1/3
C 1/4
D 1/5
E 1/6
1. OA is E.
h(100) = 2*4*6*8....*100
All prime numbers upto 50 is a factor of h(100).
For example the last prime number less than 50 is 47. 47 is a factor of 94 which is present in h(100). Any prime number greater than 50 is not a factor of h(100).
Hence, any prime number greater than 50 can be the factor of h(100)+1.
So answer is (E) greater than 40.
2. OA is (D)
Let savings be y% per month and expenses will be (100-y)% per month.
ATP, 12[y/100 *x] = 3 [(100-y)/100 * x]
Solving for y, y=20% or (1/5)
Hi, could someone double check my understanding of this.
1. We have sqrt(-x(|x|). We know x is a negative.
2. This give us sqrt(-(-x)|-x|), insert -x into x
3. We now have sqrt(x*x) or sqrt(x^2),
4. Take the square root and we are left with "x".
5. The problem tells us that "x" is negative and thus the answer is -x.
Am I correct?
1. We have sqrt(-x(|x|). We know x is a negative.
2. This give us sqrt(-(-x)|-x|), insert -x into x
3. We now have sqrt(x*x) or sqrt(x^2),
4. Take the square root and we are left with "x".
5. The problem tells us that "x" is negative and thus the answer is -x.
Am I correct?
