Math Question

Question

Hi I saw a question in the Princeton GMAT Math workout.
Page 56, 
17.What is hte value of q?
(1) q=(9)^1/2
(2) |q| = 3

This is a DS question. The answer is A. I disagree, since A means q can be +3 or -3.

Please clarify if I am missing something.

ashkg · Answer

I think if 9^0.5 is written in square root standard notation form, then that number is conisdered the positive root of that original number.

gmat2me2 · Answer

I would think there are 2 values for it and we need to consider both + and - 3 as roots of 9. So if 9^0.5 or sqrt(9) ....all are same

ashkg · Answer

Perhaps I wasn't clear before. Let me elaborate. If the square root sign is used( which is what i meant by standard notation) , it is positive. It is also called as the principal square root. You can read more about the principal square root and its notation here. https://mathworld.wolfram.com/SquareRoot.html

Antmavel · Answer

I agree with jothiip, A is not a correct answer for me. It should be E as both statements lead to 2 solutions : 3 or -3

MA · Answer

OA as A is correct.
From i, q = 3 (if q^2=9, then q = +3, or -3. but if q=sqrt(9), q has only positive value).
from ii, q can be both +3 or -3.

so A is enogh. will clearify, if any.

Antmavel · Answer

MA, I understand the way you see it but the problem doesn't specify if the value has to be +ive or -ive so for me it can be any value, maybe there was a better way to write this question because 9^1/2 can also be equal to -3. In a test day and without the OA I would have chosen E

If 9^1/2 = 3 , how do you write the same kind of expression that is equals to -3 ?

MA · Answer

i was looking for the post where i clearified the same concept to Honghu and Banerjee. but i could not find it. 

ok anyway, SQRT (9) has only one value i.e. 3. it is not like taking square root. i showed in the above post that if x^2=9, then definetly x = - 3 or +3. but if x=9^1/2, x must equal to 3 only.

Tyr · Answer

You are thinking too much guys.

q is  equal  to sqrt(9) which is 3. Period. No -3, nothing.

kapslock · Answer

Guys,

I can understand what you're saying, and reading mathworld.wolfram.com, I can understand where are you coming from, but since none of us would want to risk this in the actual GMAT, can any of you quote some other "reliable" places where a distinction has been made between the principle square root of a number and the non principle one, and by default only the principle (and the positive) square root has been considered?

Thanks

ashkg · Answer

Guys, we may be thinking too much, but this is a concept which you can't ignore because it is tested at quite a few places. As you can see people are confused here.

The most reliable place for GMAT folks is to read the OG math review, section 7 , Powers and roots of number.

It clearly says that SQRTSIGN(X) is a positive number.

Editing post to show both roots of a number:
If X is a number , it can have two square roots.
1. SQRTSIGN(X) ....this is the +ve root
2. -SQRTSIGN(X)....this is the -ve root

Antmavel · Answer

finally the question is very good ashkg :wink:

I must admit that I understand your way of thinking and the one of MA, normally we should suppose that 9^1/2 is a positive value but I have the same doubts than Kapslock, what am I suppose to answer if I face this question at the real test ?

It is not in fact an absolute answer because -3 can also be a potential one... I am gonna check the OG By the way, Tyr, your comments were useless, I don't see the interest of saying : "You are thinking too much guys. q is equal to sqrt(9) which is 3. Period. No -3, nothing." Please avoid this kind of post because this forum has been built to help people to understand the GMAT problems and the GMAT questions ; there is always a good reason behind each correct official answer and this is what we are looking for in this forum.

Tyr · Answer

What I see as a waste of time is trying to  solve  quadratic equation to find square root of given number. Quadratic equation of course has two roots, square root is just a single number.

Square root of a number is  defined  as positive number.
Yes, math defines lots of things, and no you don't want to overthink defenitions or you will end up with different geometry.

gmat2me2 · Answer

guys in inequalities when we say if x^2 >9 then x>3 or -3 then why are we saying it is only positive in this case.....No let our fundas be consistent rather than case/problem dependent.

I would argue A is wrong in this problem

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