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## Need help - Data sufficiency

This topic has 4 member replies
momentary_lapse Senior | Next Rank: 100 Posts
Joined
26 Feb 2007
Posted:
43 messages

#### Need help - Data sufficiency

Wed May 09, 2007 9:36 pm
Hi,

If m and n are both positive, what is the value of m * sq rt(n)?

1) mn / sq rt (n) = 10
2) ((m^2) * n)/2 = 50

The first option I can understand. If m and n are +ve the only way the expression can be +ve = 10 is if sq rt n is +ve. Therefore 1 is sufficent

For part 2 if sq rt of n is negative, then m^2 * n can still be +ve. ex: if m = 5 and n = 4 then the expression is (25*4)/2 = 50. But by x-multiplying with 2 we get (m^2)*n = 100. So if we take the square root on both sides we get m *sq rt of n which may be + or - 2 . So the answer could be + or - 10.

thanks

momentary_lapse Senior | Next Rank: 100 Posts
Joined
26 Feb 2007
Posted:
43 messages
Thu May 10, 2007 1:16 am
Okay all.. I have figured it out after significant research. We have missed out an important concept here as well in another post by me under the GMAT Math forum.

The square root in the questions which are written with the square root symbol is actually called a radical. I wasnt able to figure out how to type it which is why i was writing square root.

So when we say √a we actually mean the non negative value of the square root of a. This is totally different from solving an equation where x^2 = 25 and therefore x=+5 or -5

When a is negative √a is = |a| and therefore in the case of the question where we are asked to find the √(-a|a|) it is = √a^2 which is = |a| and since a ia negative the answer is -a.

http://www.jcoffman.com/Algebra2/ch7_1.htm

This is an important concept which i learnt and i feel much more at ease now

Apologies if people knew about this and got confused because of the problem being written as "find the square root" instead of "find √"

thanks

mendiratta Junior | Next Rank: 30 Posts
Joined
08 May 2007
Posted:
26 messages
1
Wed May 09, 2007 11:50 pm
Valid point.
I also agree that it can be + or - 10.

jayhawk2001 Community Manager
Joined
28 Jan 2007
Posted:
789 messages
Followed by:
1 members
30
Wed May 09, 2007 9:50 pm
momentary_lapse wrote:
Hi,

If m and n are both positive, what is the value of m * sq rt(n)?

1) mn / sq rt (n) = 10
2) ((m^2) * n)/2 = 50

The first option I can understand. If m and n are +ve the only way the expression can be +ve = 10 is if sq rt n is +ve. Therefore 1 is sufficent

For part 2 if sq rt of n is negative, then m^2 * n can still be +ve. ex: if m = 5 and n = 4 then the expression is (25*4)/2 = 50. But by x-multiplying with 2 we get (m^2)*n = 100. So if we take the square root on both sides we get m *sq rt of n which may be + or - 2 . So the answer could be + or - 10.

thanks
I guess there's a small difference here

sqrt(n) is always positive, by definition.

But if you have x^2 = n, then x can be +sqrt(n) or -sqrt(n)

momentary_lapse Senior | Next Rank: 100 Posts
Joined
26 Feb 2007
Posted:
43 messages
Wed May 09, 2007 10:56 pm
how is it always +ve? this is what i dont get? if n is +ve why should the sq rt always +ve?

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