hypocritical ETS - DS

Question

x^2 = 16 is x = 4 

based on ETS we dont know becuase x could be + or - 4

however sqrt(16) = 4 (+ 4 only)

so if you take dqrt on both side of above eqn it follows that x = 4

so are we supposed to assume on solution only when we have sqrt given to us?

SigEpUCI · Answer

I'm not exactly sure what you are asking, but you should always consider plus and minus roots, unless told not to do so.

ian7777 · Answer

There is actually a very clear distinction on the test.

The square root of a number is always positive, and when solving for x when given x^2, the answer is always positive or negative.

So SQRT 16 = 4 while 
when x^2=16, x = +/- 4

I can explain this this way:

Take x^2=9. From there we can say that x^2 - 9 = 0, or (x+3)(x-3) = 0. So x must equal both plus and minus 3.

But SQRT 9 is a positive, irrational number. So it must be three. I can also ask for the -(SQRT 9), in which case the answer would be -3.

This is always true, and you can count on it for the test.

smcgrath12 · Answer

Thanks for explaining that. I have a follow up question. Is there any difference between SQ ROOT of 4 and 4^1/2, in terms of whether the answer is just 2 or 2 and -2?

ian7777 · Answer

nope. the only time it could go negative is in algebra. The example you put up there is a positive number.

ywilfred · Answer

I've read somewhere that for GMAT, only the positive value of a sqrt is valid.

hardworker_indian · Answer

Wow, I never realised this. Thanks Ian.

ian7777 · Answer

There is a very hard question that exemplifies this reality. Check out the OG DS 260:

Is SQRT  = 5 - x?

1) -x|x| > 0

2) 5 - x > 0

Anonymous · Answer

I am getting it as D (Both are individually sufficient).

If I am wrong, Could you explain me why?

I check the stuff in the OG today itself.

Thanks..

longhorn2020 · Answer

Is the answer D?
basically, 
(1) states that x is negative
(2) states that x<5

either one can validate the stimulus

hypocritical ETS - DS

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