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Is n > 6 ?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Oct 29, 2013 5:47 am
informmefast wrote:
Is n > 6?

1) √n > 2.5
2) n > √37
Target question: Is n > 6?

Statement 1: √n > 2.5
Since 2.5 = √6.25, we can write √n > √6.25
This tells us that n > 6.25, which means n is definitely greater than 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > √37
We know that √37 > √36, so we can write n > √37 > √36
In other words, n > √37 > 6
As we can see, n is definitely greater than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by mevicks » Tue Oct 29, 2013 5:50 am
informmefast wrote: Is n > 6?
1) √n > 2.5
2) n > √37
Note: On the gmat √x = +ive root
Thus if the gmat says √ some number its always positive! :|

Q: n > 6?

St1:
√n > 2.5
Squaring both sides:
n > 6.25
Thus n will always be greater than 6 SUFFICIENT

St2:
n > √37
Now √36 = 6
√36 < √37
Thus n > 6
SUFFICIENT

Answer D
Last edited by mevicks on Tue Oct 29, 2013 5:58 am, edited 1 time in total.
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by informmefast » Tue Oct 29, 2013 5:53 am
Brent@GMATPrepNow wrote:
informmefast wrote:
Is n > 6?

1) √n > 2.5
2) n > √37
Target question: Is n > 6?

Statement 1: √n > 2.5
Since 2.5 = √6.25, we can write √n > √6.25
This tells us that n > 6.25, which means n is definitely greater than 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > √37
We know that √37 > √36, so we can write n > √37 > √36
In other words, n > √37 > 6
As we can see, n is definitely greater than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent


Hi Brent,
I understood that statement 1 is sufficient but regarding statement 2 I have the following query -

n > √37
Therefore n > +/- 6.08 since root of a number gives both positive and negative values. How does it satisfy n > 6 ?
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by Brent@GMATPrepNow » Tue Oct 29, 2013 5:54 am
Aside: Some students will answer this question incorrectly if they believe that the square root of a number can be negative. For example, some students believe that √36 = 6 or -6
However, this is not the case. The square root notation (√) is essentially asking us to identify the positive value that, when squared, equals 36

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by Brent@GMATPrepNow » Tue Oct 29, 2013 5:58 am
informmefast wrote: Hi Brent,
I understood that statement 1 is sufficient but regarding statement 2 I have the following query -

n > √37
Therefore n > +/- 6.08 since root of a number gives both positive and negative values. How does it satisfy n > 6 ?
It looks like I was answering your question while you were writing it. :-)

By the way, here's how the Official Guide puts it: √n denotes the positive number whose square is n.

Cheers,
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by mevicks » Tue Oct 29, 2013 6:05 am
informmefast wrote: n > √37
Therefore n > +/- 6.08 since root of a number gives both positive and negative values. How does it satisfy n > 6 ?
My 2 cents on this...

The best way around this problem is to memorize this :
This is a part of the test that confuses people. Here are the GMAT rules about this:
1) The square root of a number is the positive number only. Thus, the square root of 16 is ONLY positive 4 on the GMAT.
*however*
2) If I have x^2 = 16, then x could be 4 or -4
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by GMATGuruNY » Tue Oct 29, 2013 6:46 pm
Is n > 6?

1) √n > 2.5
2) n > √37
Statement 1: √n > 2.5
Squaring both sides, we get:
n > (5/2)²
n > 25/4.
n > 6.25.
Thus, n > 6.
SUFFICIENT.

Statement 2: n > √37
Squaring both sides of the question stem, we can rephrase it as follows:
Is n² > 36?
Squaring both sides of statement 2, we get:
n² > 37.
Thus, n² > 36.
SUFFICIENT.

The correct answer is D.
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by sanju09 » Tue Oct 29, 2013 10:24 pm
mevicks wrote:
informmefast wrote: Is n > 6?
1) √n > 2.5
2) n > √37
Note: On the gmat √x = +ive root
Thus if the gmat says √ some number its always positive! :|

Q: n > 6?

St1:
√n > 2.5
Squaring both sides:
n > 6.25
Thus n will always be greater than 6 SUFFICIENT

St2:
n > √37
Now √36 = 6
√36 < √37
Thus n > 6
SUFFICIENT

Answer D
Not on GMAT only, it's a universally accepted fact that any positive thing inside √ only brings a positive result out. It's probably a 420 score question of GMAT. :)
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by informmefast » Thu Nov 14, 2013 6:43 pm
Brent@GMATPrepNow wrote:
informmefast wrote: Hi Brent,
I understood that statement 1 is sufficient but regarding statement 2 I have the following query -

n > √37
Therefore n > +/- 6.08 since root of a number gives both positive and negative values. How does it satisfy n > 6 ?
It looks like I was answering your question while you were writing it. :-)

By the way, here's how the Official Guide puts it: √n denotes the positive number whose square is n.

Cheers,
Brent

Hi Brent,
This is a question that I faced in the Kaplan Mock -

What is the average (arithmetic mean) of A, B, and 4C?

(1) A + B = 17

(2) C(sqr) = 49


Here going by gmat rules I should be considering only C = 7 (only the positive rule) and the final answer should have been (c) i.e both statements together is sufficient. But the solution provided states (e) as the answer since c has been considered to be equal to 7 or -7 . Please clarify.
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by informmefast » Thu Nov 14, 2013 6:49 pm
Hi..sorry for not observing mevicks explanation. I think I got the point now. Thanks.
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