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replayyyy: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Tue Aug 24, 2010 5:16 am

by replayyyy » Wed Nov 03, 2010 4:35 am

If x<0, then second square of -x*|x| is

-x
-1
0
x
second square of x

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Source: Beat The GMAT — Problem Solving | Wed Nov 03, 2010 4:35 am

diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Wed Nov 03, 2010 5:22 am

replayyyy wrote:If x<0, then second square of -x*|x| is

-x
-1
0
x
second square of x

is second square meant squareroot?

because x is negative |x|=-x and -(-x)=x so the second suare of x*-x=-x
the answer is A

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replayyyy: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Tue Aug 24, 2010 5:16 am

by replayyyy » Wed Nov 03, 2010 5:43 am

diebeatsthegmat wrote:
replayyyy wrote:If x<0, then second square of -x*|x| is

-x
-1
0
x
second square of x
is second square meant squareroot?

because x is negative |x|=-x and -(-x)=x so the second suare of x*-x=-x
the answer is A

yes, it is squareroot, my mistake

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rkanthilal: Master | Next Rank: 500 Posts; Posts: 154; Joined: Thu Aug 26, 2010 9:32 amFollowed by: 19 members; Location: Chicago,IL; Thanked: 46 times; GMAT Score:760

by rkanthilal » Wed Nov 03, 2010 8:09 am

I'm getting D for this one.

If X<0

-(-x)*|x|=x^2
sqrt x^2 = x

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gtestprep: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Thu Jun 24, 2010 3:56 am; Thanked: 3 times

by gtestprep » Wed Nov 03, 2010 9:22 am

rkanthilal wrote:I'm getting D for this one.

If X<0

-(-x)*|x|=x^2
sqrt x^2 = x

Yep. That's right, if x < 0 then |x| = - x. So the equation becomes -x * -x = x ^2
The square-root of x^2 = +x

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Wed Nov 03, 2010 9:44 am

gtestprep wrote:
rkanthilal wrote:I'm getting D for this one.

If X<0

-(-x)*|x|=x^2
sqrt x^2 = x
Yep. That's right, if x < 0 then |x| = - x. So the equation becomes -x * -x = x ^2
The square-root of x^2 = +x

you guys forget a negative mark... its squareroot of (-x)|x|
so solve the (-x) first : if x is negative so (-x) will be [-(-x)]=x
x<0 so |x|=-x
so squareroot of (-x)x=-square root of x^2=-x
the answer must be A

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rkanthilal: Master | Next Rank: 500 Posts; Posts: 154; Joined: Thu Aug 26, 2010 9:32 amFollowed by: 19 members; Location: Chicago,IL; Thanked: 46 times; GMAT Score:760

by rkanthilal » Wed Nov 03, 2010 10:49 am

diebeatsthegmat wrote:
gtestprep wrote:
rkanthilal wrote:I'm getting D for this one.

If X<0

-(-x)*|x|=x^2
sqrt x^2 = x
Yep. That's right, if x < 0 then |x| = - x. So the equation becomes -x * -x = x ^2
The square-root of x^2 = +x
you guys forget a negative mark... its squareroot of (-x)|x|
so solve the (-x) first : if x is negative so (-x) will be [-(-x)]=x
x<0 so |x|=-x
so squareroot of (-x)x=-square root of x^2=-x
the answer must be A

You are correct. The answer is A.

For example, if x=-2
sqrt(-x*|x|)=sqrt(-(-2)*|-2|)=sqrt(2*2)=2

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rros0770: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Mar 14, 2008 1:39 pm; Thanked: 3 times

by rros0770 » Wed Nov 03, 2010 1:25 pm

Confused slightly here. rkanthilal, you proved the answer to be (D) which is x

Hey Die, I'm looking at your explanation:
you guys forget a negative mark... its squareroot of (-x)|x|
so solve the (-x) first : if x is negative so (-x) will be [-(-x)]=x
x<0 so |x|=-x

Wouldnt the value of Absolute (x) be the positive value of (x), being that absolute value is essentially the distance between a given number and zero ? For example:

|3|= 3
|-4|= 4

so, being that we know (X) is negative, the absolute value would make it a positive. Essentially we'd get end up with 2 positive values for (X), and the sqroot root would leave us with choice D which is (X)

Just wanted to clarify, am I missing some sort of principle or rule here?

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Wed Nov 03, 2010 5:24 pm

rkanthilal wrote:
diebeatsthegmat wrote:
gtestprep wrote:
rkanthilal wrote:I'm getting D for this one.

If X<0

-(-x)*|x|=x^2
sqrt x^2 = x
Yep. That's right, if x < 0 then |x| = - x. So the equation becomes -x * -x = x ^2
The square-root of x^2 = +x
you guys forget a negative mark... its squareroot of (-x)|x|
so solve the (-x) first : if x is negative so (-x) will be [-(-x)]=x
x<0 so |x|=-x
so squareroot of (-x)x=-square root of x^2=-x
the answer must be A
well, if its a real number for x such as x= 2 or -2
things will be different, the answer, i meant... so yes, you
You are correct. The answer is A.

For example, if x=-2
sqrt(-x*|x|)=sqrt(-(-2)*|-2|)=sqrt(2*2)=2

well, if its a real number for x such as x= 2 or -2
things will be different, the answer, i meant will be different, the answer will be always a positive number for any real negative/positive number,,,

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rkanthilal: Master | Next Rank: 500 Posts; Posts: 154; Joined: Thu Aug 26, 2010 9:32 amFollowed by: 19 members; Location: Chicago,IL; Thanked: 46 times; GMAT Score:760

by rkanthilal » Wed Nov 03, 2010 6:42 pm

rros0770, I think you are making the same error that I originally did. Yes, since X<0 when we multiply -x and |x| we are multiplying two positive numbers. Then when we take the sqrt of that number we end up with another positive number.

If (D) is correct and the answer is X, then that would mean the result is negative (since x is a negative number). I think the confusion is because we are giving the answer in terms of X. Substitute an actual number and it becomes clearer.

For example, if x=-2
sqrt-x*|x|
sqrt-(-2)*|-2|
sqrt(2*2)=2

Here x=-2. The result of the equation is positive 2. If we are to give the result in terms of x, the answer is -x (since x is negative).

Hope that helps...

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Nov 04, 2010 4:30 am

replayyyy wrote:If x<0, the square root of -x*|x| is

-x
-1
0
x
second square of x

Hi guys,

Let me show you how to "deal" with absolute values (modulus) without "suffering"...

From the fact that x is negative, we know that |x| = -x (and please note that here "- x" is the opposite of a negative number, therefore here we are sure "- x" is POSITIVE).

Therefore -x |x| = -x (-x) = x^2 and finally, remembering that: sqrt (x^2) = |x| we have (in this case) that sqrt(x^2) = |x| = -x, and we are done.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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