BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

sqrroot negative number x absolute value

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Sat Jun 14, 2008 5:12 am
Thanked: 1 times

sqrroot negative number x absolute value

by jopup » Mon Jun 16, 2008 10:44 pm
Image

how do you do this?
how can you square root a negative number???
wont negative x times absolute value be negative?
what ami missing here?


edit:
***get it now, thanks [gee, thats tricky]***
Last edited by jopup on Wed Jun 18, 2008 8:54 am, edited 1 time in total.
Top
Source: — Problem Solving |
Legendary Member
Posts: 631
Joined: Mon Feb 18, 2008 11:57 pm
Thanked: 29 times
Followed by:3 members

by netigen » Tue Jun 17, 2008 12:29 am
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
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Sun Jun 15, 2008 10:50 pm
Thanked: 4 times

by Motherjane » Tue Jun 17, 2008 5:45 am
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
Top
Legendary Member
Posts: 621
Joined: Wed Apr 09, 2008 7:13 pm
Thanked: 33 times
Followed by:4 members

by vittalgmat » Tue Jun 17, 2008 1:04 pm
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
Hi,
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
Top
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Sat Jun 14, 2008 5:12 am
Thanked: 1 times

by jopup » Tue Jun 17, 2008 1:45 pm
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?)
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680

by II » Tue Jun 17, 2008 2:49 pm
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?)
Let me try to add some clarity here:
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.
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Sun Jun 15, 2008 10:50 pm
Thanked: 4 times

by Motherjane » Tue Jun 17, 2008 2:53 pm
vittalgmat wrote:
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
Hi,
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
Hi 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.
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Mon Jun 16, 2008 10:26 am

New questions to solve

by bluefalcon_7691 » Wed Jun 18, 2008 6:44 am
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
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

by gabriel » Wed Jun 18, 2008 7:34 am
@bluefalcon .. start 2 new threads for each of the two questions. Please do not continue discussing them on this thread. Also use the "search" function the first questions has been discussed several times on the forum

Regards
Top
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Sat Jun 14, 2008 5:12 am
Thanked: 1 times

by jopup » Mon Jun 23, 2008 12:56 am
this question is still concerning me

sqrt of ( x lxl) is + x OR -x

why is - x the answer?
Top
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

by AleksandrM » Mon Jun 23, 2008 9:03 am
If x^2 = 4, then x = +2 or -2, you know that x < 0, then x = -2.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680

by II » Fri Jun 27, 2008 11:51 am
AleksandrM wrote:If x^2 = 4, then x = +2 or -2, you know that x < 0, then x = -2.
Good, simple, explanation ! :-)
Top
Senior | Next Rank: 100 Posts
Posts: 39
Joined: Sun Jun 15, 2008 10:50 pm
Thanked: 4 times

Re: New questions to solve

by Motherjane » Sat Jun 28, 2008 2:06 pm
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)
Top
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Tue Jul 01, 2008 11:54 am
Location: San Diego

by somail » Tue Jul 01, 2008 3:02 pm
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?
Top
Master | Next Rank: 500 Posts
Posts: 144
Joined: Thu Apr 17, 2008 3:33 pm
Thanked: 8 times

by Sunny22uk » Tue Jul 01, 2008 5:16 pm
The answer should be -x as the question says x<0, the positive solution can be discarded.
Top
Post new topic Post Reply