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VP  Joined: 29 Dec 2005
Posts: 1246

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vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,
answer should be "-x".

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

(I) x^2 = 25
(II) x = square root 25

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232
http://www.jamesbrennan.org/algebra/rad ... _roots.htm

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.
SVP  Joined: 14 Dec 2004
Posts: 1558

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Professor wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,
answer should be "-x".

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

(I) x^2 = 25
(II) x = square root 25

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232
http://www.jamesbrennan.org/algebra/rad ... _roots.htm

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.

What is the difference between (I) & (II)? I guess we arrive on (II) from (i) itself. I have a very uneasy feeling on this.
VP  Joined: 29 Dec 2005
Posts: 1246

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vivek123 wrote:
Professor wrote:
lets see the following examples:
(I) x^2 = 25
(II) x = square root 25

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232
http://www.jamesbrennan.org/algebra/rad ... _roots.htm

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.

What is the difference between (I) & (II)? I guess we arrive on (II) from (i) itself. I have a very uneasy feeling on this.

if x^2 = 25, x can be both +ve and -ve but if x = square root (25) x can only be 5, not -5. thats it. i told you it is in OG but where? i am trying to find it. once i get it, i will let you know.
Manager  Joined: 01 Feb 2006
Posts: 89

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Professor wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,
answer should be "-x".

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

(I) x^2 = 25
(II) x = square root 25

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232
http://www.jamesbrennan.org/algebra/rad ... _roots.htm

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.
i believe u have it mistaken. i'm sure i've seen cases contrary to your explanation for (II)
Intern  Joined: 14 Feb 2006
Posts: 16
Square roots  [#permalink]

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Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

The question is x<0 ,sqr (-x * l x l= ?

let x be -2

sqr ( 2* l-2l)= sqr( 2*2)= sqr(4) = 2

since x is -2 , 2 is -x.

That is it.
SVP  Joined: 14 Dec 2004
Posts: 1558
Re: Square roots  [#permalink]

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INSEAD1979 wrote:
Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

This is something that I really wonder. It sounds like "whether" is preferred over "if" in GMAT You guys might be correct, I'll really appreciate if you can PLEASE clarify on this part Director  Joined: 17 Dec 2005
Posts: 522
Location: Germany
Re: Square roots  [#permalink]

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INSEAD1979 wrote:
Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

You aren't right. The square root of a negative number isn't mathematically defined.

As Professor said:

(I) x^2 = 25
(II) x = square root 25

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

Of course if you consider sqrt (x^2) x can be positive or negative.

Hope that clarifies
SVP  Joined: 05 Apr 2005
Posts: 1571
Re: Square roots  [#permalink]

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allabout wrote:
The square root of a negative number isn't mathematically defined.

As Professor said:
(I) x^2 = 25
(II) x = square root 25

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

the important concept is: sqrt (x) has only one value i.e. +ve.

x = sqrt (25) = only 5.
x^2 = 25 = 5 or -5.
Manager  Joined: 01 Feb 2006
Posts: 89
Re: Square roots  [#permalink]

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HIMALAYA wrote:
allabout wrote:
The square root of a negative number isn't mathematically defined.

As Professor said:
(I) x^2 = 25
(II) x = square root 25

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

the important concept is: sqrt (x) has only one value i.e. +ve.

x = sqrt (25) = only 5.
x^2 = 25 = 5 or -5.
i really don't understand the thinking behind this. why would sqrt have only one value?
Intern  Joined: 14 Feb 2006
Posts: 16
sqr root  [#permalink]

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I repeat

Square root of 25 in GMAT: 5 ,nothing else.

BUT if you wanna go and check high math books,you can see that it can be -5.

What I dont understand : Why you guys lose time with unimportant stuff. Look at my solution. The answer to the original question is -x. And that is it. It has nothing to do with sqrt of 25 = 5 or -5!

p.s: By the way, if is only correct if it is used to convey the meaning of a possibility. Whether is always correct when you talk about alternatives.
Manager  Joined: 01 Feb 2006
Posts: 89
Re: sqr root  [#permalink]

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INSEAD1979 wrote:
I repeat

Square root of 25 in GMAT: 5 ,nothing else.

BUT if you wanna go and check high math books,you can see that it can be -5.

What I dont understand : Why you guys lose time with unimportant stuff. Look at my solution. The answer to the original question is -x. And that is it. It has nothing to do with sqrt of 25 = 5 or -5!

p.s: By the way, if is only correct if it is used to convey the meaning of a possibility. Whether is always correct when you talk about alternatives.
If it's unimportant you don't have to bother replying the thread.
SVP  Joined: 05 Apr 2005
Posts: 1571
Re: Square roots  [#permalink]

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guys, lets be polite and respectful to each other in expressing our views. its one's freedom whether to take the views expressed here.

I also agree with that SQRT (25) = 5. but the reason .

i believe Honghu can explain.
SVP  Joined: 03 Jan 2005
Posts: 2059

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Square root of any positive number is a positive number. When we say x^2=a, we know that x=+/-sqrt(a). You can see that sqrt(a) itself is positive, but x could be positive sqrt(a) or negative sqrt(a).

Using an example, say x^2=25. We know that x=+/-sqrt(25), where sqrt(25)=5.

Hope this helps. _________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
Director  Joined: 04 Jan 2006
Posts: 891

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square root of a positive number is a positive number..

x^2 = 4, x = + or -2
if x = sqrt(4), x = 2
nothing else.
sqrt(-4) = 2i

so in this case.. the answer is sqrt(-x|x|)
since x is < 0,so pick x = -4, we have sqrt(-(-4)*|-4|)
==> 4

This is what I learnt at school.. Now I am totally lost if this IS WRONG.
Please explain!!!!!!!!!!!!!!!!
Senior Manager  Joined: 05 Jan 2006
Posts: 369

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Just to End this discussion let me quote from the bible (OG-11, Page 126)

9. Absolute Value
The absolute value of x is denoted |x|, is defined to be x if x>=0 and â€“x is x<0. Note that sqrt(x^2) denotes that nonnegative square root of x^2 and so sqrt(x^2) = |x|

Following this answer of the question should be â€“x, as x is already negative and we need positive answer.

I hope this helps.
SVP  Joined: 03 Jan 2005
Posts: 2059
Re: absolute value  [#permalink]

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believe2 wrote:
if x <0 , then sqrt (-x |x|) equals

1. -x
2. -1
3. 1
4. x
5. sqrt(x)

If x<0, the |x|=-x. sqrt(-x|x|)=sqrt((-x)^2)=-x.

Look at the options, you know that 2 and 3 can be thrown out right away. sqrt(x) is wrong because for GMAT only positive number can be inside a square root. Compare 1 and 4, you want a positive number, which would be -x since x is negative.
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
SVP  Joined: 14 Dec 2004
Posts: 1558
Re: absolute value  [#permalink]

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HongHu wrote:
believe2 wrote:
if x <0 , then sqrt (-x |x|) equals

1. -x
2. -1
3. 1
4. x
5. sqrt(x)

If x<0, the |x|=-x. sqrt(-x|x|)=sqrt((-x)^2)=-x.

Look at the options, you know that 2 and 3 can be thrown out right away. sqrt(x) is wrong because for GMAT only positive number can be inside a square root. Compare 1 and 4, you want a positive number, which would be -x since x is negative.

I guess this is how I arrived at my answer -x But I was totally confused with what is needed in GMAT etc.

Anyways, thanks Hong Cheers
VP  Joined: 29 Dec 2005
Posts: 1246

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HongHu wrote:
Square root of any positive number is a positive number. When we say x^2=a, we know that x=+/-sqrt(a). You can see that sqrt(a) itself is positive, but x could be positive sqrt(a) or negative sqrt(a).

Using an example, say x^2=25. We know that x=+/-sqrt(25), where sqrt(25)=5.

Hope this helps. i just want to be/make clear on why sqrt (25) = 5.

suppose x^2 = 25
x = sqrt (25) or - sqrt (25)
and we are here dealing with only "sqrt (25)".

therefore, sqrt (25) = 5

thank you honghu.
Director  Joined: 04 Jan 2006
Posts: 891

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I still dont understand..

isnt |x| just the positive value of the number x?
VP  Joined: 21 Sep 2003
Posts: 1005
Location: USA

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willget800 wrote:
I still dont understand..

isnt |x| just the positive value of the number x?

Yes. But what if the x is -ve (say x = -2), then the absolute value of x is 2
x = -2
|x| = 2 = -(-2) = -x

For more gyan (Hindi word for knowledge) see..

http://www.purplemath.com/modules/absolute.htm
_________________
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds 21 Mar 2006, 09:41

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