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# Math Question

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Intern
Joined: 30 Mar 2005
Posts: 2

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24 Apr 2005, 11:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.
Senior Manager
Joined: 21 Mar 2004
Posts: 445
Location: Cary,NC

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24 Apr 2005, 16:58
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.
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ash
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I'm crossing the bridge.........

Director
Joined: 18 Feb 2005
Posts: 669

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24 Apr 2005, 18:35
ashkg wrote:
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.

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
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Joined: 21 Mar 2004
Posts: 445
Location: Cary,NC

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24 Apr 2005, 18:46
gmat2me2 wrote:
ashkg wrote:
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.

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

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.
http://mathworld.wolfram.com/SquareRoot.html
Attachments

sqrt.JPG [ 29.24 KiB | Viewed 1054 times ]

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ash
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I'm crossing the bridge.........

VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

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24 Apr 2005, 19:05
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
VP
Joined: 25 Nov 2004
Posts: 1483

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24 Apr 2005, 20:26
jothiip wrote:
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.

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.
VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
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24 Apr 2005, 22:11
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 ?
VP
Joined: 25 Nov 2004
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24 Apr 2005, 22:38
Antmavel wrote:
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 ?

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.
Manager
Joined: 22 Apr 2005
Posts: 129
Location: Los Angeles

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25 Apr 2005, 10:21
You are thinking too much guys.

q is equal to sqrt(9) which is 3. Period. No -3, nothing.
Senior Manager
Joined: 15 Mar 2005
Posts: 418
Location: Phoenix

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25 Apr 2005, 11:50
Tyr wrote:
You are thinking too much guys.

q is equal to sqrt(9) which is 3. Period. No -3, nothing.

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
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Senior Manager
Joined: 21 Mar 2004
Posts: 445
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25 Apr 2005, 16:42
kapslock wrote:
Tyr wrote:
You are thinking too much guys.

q is equal to sqrt(9) which is 3. Period. No -3, nothing.

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

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
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ash
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I'm crossing the bridge.........

Last edited by ashkg on 25 Apr 2005, 18:58, edited 1 time in total.
VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

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25 Apr 2005, 18:23
finally the question is very good ashkg 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.
Manager
Joined: 22 Apr 2005
Posts: 129
Location: Los Angeles

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25 Apr 2005, 22:31
Antmavel wrote:
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.

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.
Director
Joined: 18 Feb 2005
Posts: 669

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26 Apr 2005, 04:27
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
26 Apr 2005, 04:27
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