# Thread: Ps set 11 q 7

1. ## Ps set 11 q 7

If x < 0 , SQRT ( -x . |x|)
1) -x
2) -1
3) 1
4) x
5) sqrt(x)

SPOILER: OA A. I guess its D. Am I missing something here  Reply With Quote

2. I X I = positive. so, (-X . I X I) means (- (-). +) or positive. sqrt of positive is positive. IMO D.  Reply With Quote

3. Originally Posted by shyamprasadrao If x < 0 , SQRT ( -x . |x|)
A) -x
B) -1
C) 1
D) x
E) sqrt(x)
A quick way to solve this question is to plug in a value for x.
Since x<0, let's say that x= -5

So, the sqrt[-x (|x|)] = sqrt[5 (|-5|)] = sqrt[5(5)] = sqrt = 5

Answer choice A is -x, so if x= -5, then -x = 5. Since our output above is 5, answer choice A is correct.

Cheers,
Brent  Reply With Quote

4. wonderful......thanks Brent  Reply With Quote

5. What we are finding here ? sqrt (- x.|x|) = ? right ?.
As x is negative - x is supposed to be positive . That means X. Besides, | - x| = x.
so sqrt (-x.|x|)= sqrt (x.x) = sqrt (x^2) = x. The option is D.

Please point out the my mistake.  Reply With Quote

6. Hey 800, You have presupposed that x is negative, i.e -x and you are calculation leads to x, which is positive in sign. Hence you need -(-x )....

Even simpler, lets assume, x to be -y , you have SQRT ( -(-y) . | -y | ) = SQRT (y^2 ) = Y.... But what is y ??? -x..... Hence answer is A.

Thanks Brent for the explanation.  Reply With Quote

7. Originally Posted by shyamprasadrao Hey 800, You have presupposed that x is negative, i.e -x and you are calculation leads to x, which is positive in sign. Hence you need -(-x )....

Even simpler, lets assume, x to be -y , you have SQRT ( -(-y) . | -y | ) = SQRT (y^2 ) = Y.... But what is y ??? -x..... Hence answer is A.

Thanks Brent for the explanation.
No. But I have calculated x with negative sign. Why should I add another negative sign after calculation. Please explain. I think in G-day I will commit same mistake if I am not clear.  Reply With Quote

8. Yes I got the point !!! I missed the basic of roots!
Rule: a root can only have a negative value if 1. it is an odd root and 2. the base of the root is negative. Here I had to apply the second condition of the rule.
Thanks Brent & shyamprasadrao to inspire me to review the basic.

Cheers !!!  Reply With Quote

9. Hi,

I just needed 1 clarification...as far as GMAT is concerned, is sqrt(100) = 10??? Or is sqrt(100) = +/- 10???  Reply With Quote

10. The square root of any number (by definition) is always positive (or zero in the case of sqrt(0)=0).
So, sqrt(100)=10, sqrt(49)=7, . . . etc.

Cheers,
Brent  Reply With Quote