If a < 0, then sqr rt -a * [a] is ?

[nwaneri.michael]

If a < 0, then sqr rt -a * [a] is ?

while this problem originally had variable x, I changed it to a to minimize confusion.

[a] = absolute value of a.

Question reads under radical sign: -a times absolute value of a. With a < 0.

Answers
-a
-1
1
a
sqr rt a.

I thought that if a was less than 0, then clearly a must be negative. So -a= negative times negative which equals positive a times absolute value of a which by rule has to be positive. So positive times positive = a^2 and under radical sign, a^2 = a. For that reason I chose answer a for the answer and was shocked to learn that -a (being -x was actually the answer). What am I doing wrong here? Thanks in advance.

[sejal.vaidya]

Hi,

The answer to the mathematical operation sqrt(-a*|a|) is a. Now since a > 0, the answer in terms of given data is -a. So, the answer is a positive value which is opposite sign of givn sign of a.

Thanks,
Sejal.

[nwaneri.michael]

Thank you Sejal. But that answer you suggested is the one I chose and it is wrong. And also a < 0 and not a > 0.

Can a manhattan gmat staff please respond to this question for a fellow course student. This issue is still unresolved.

Michael

[RonPurewal]

first thing:
you're taking the square root of the WHOLE expression, right?
as in, you're taking the square root of the product of -A and |A|?

if that's the case, then, yes, -A times |A| is just A squared (since each of those things is the opposite of whatever A is).
therefore, the square root is √(A^2), which equals |A|.
since A is negative, |A| is the same thing as -A.
therefore, -A is the correct answer.

--

you can also solve the problem by plugging in your own number for A, say, -5.
then, assuming as before that you're taking the square root of the whole product, this is the square root of (5 x 5), which is 5.
if A = -5, then only the first choice equals 5, so that's the correct answer.

--

if you're claiming that the "correct" answer was one of the other choices, then which choice was supposedly the correct one?
...and could you post a screen shot to prove it?
(this is general protocol around here, by the way: if you're going to say that a problem has a "surprising answer", then you should of course say what that answer actually is.)