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Value of n

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by Deepthi Subbu » Sun Sep 01, 2013 8:25 am
Is n > 6?

1. sqrt(n) > 2.5
2.n > sqrt(37)

[spoiler]I see A is sufficient. However, when it comes to st 2 , n > sqrt(37) translates to n^2 > 6 . So n is either greater than 6 or less than -6. So the answer must be A right?[/spoiler]
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Source: — Data Sufficiency |
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by vinay1983 » Sun Sep 01, 2013 8:49 am
Hmm, I feel it is as below:

Statement A

Sqrt(n) > 2.5

This can mean N can also be 6 or 7 or 8 Not sufficient


Statement B

N > sqrt (37)

Sqrt 37 yields little more than 6, hence N has to be more than 6 Sufficient
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Sun Sep 01, 2013 9:56 am
Deepthi Subbu wrote:Is n > 6?

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

Statement 1: √n > 2.5
Since (2.5)² = 6.25, we know that √6.25 = 2.5
If √n is GREATER THAN 2.5, we know that n must be GREATER THAN 6.25
So, 6.25 < n
Since 6 < 6.25, we get 6 < 6.25 < n
So, it must be the case that Is 6 < n
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > √37
We know that √36 < √37
So, if √37 < n, we can write √36 < √37 < n
So, √36 < n
Since √36 = 6, we can be certain that 6 < n
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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by Java_85 » Sun Sep 01, 2013 11:50 am
Definitely D!
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by [email protected] » Sun Sep 01, 2013 1:10 pm
Hi Deepthi Subbu,

By definition, the square root of a number can only be POSITIVE.

So sqrt(37) must be positive and a little greater than 6.

By comparison, if you were told that N^2 > 6, then N COULD BE positive or negative.

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by [email protected] » Sun Sep 01, 2013 1:13 pm
Hi vinay1983,

I hope you read through Bren't explanation, because you made a math mistake in your approach and it would have cost you this question.

Since (2.5)^2 = 6.25, Fact 1 proves that n > 6 and would be considered SUFFICIENT on its own!

You must be willing to do the necessary math (and do it correctly) if you want to hit 700+ on Test Day.

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by vinay1983 » Sun Sep 01, 2013 8:42 pm
[email protected] wrote:Hi vinay1983,

I hope you read through Bren't explanation, because you made a math mistake in your approach and it would have cost you this question.

Since (2.5)^2 = 6.25, Fact 1 proves that n > 6 and would be considered SUFFICIENT on its own!

You must be willing to do the necessary math (and do it correctly) if you want to hit 700+ on Test Day.

GMAT assassins aren't born, they're made,
Rich
Yes you are right, this was a yes/no question.I mistook it for a value question!Point taken!
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by ani781 » Mon Sep 02, 2013 6:46 am
Hi ,
I am little confused with the statement D.
Why is it not that n > 36^1/2 => n > +6 / -6.

Is not sqrt of 36 = +/- 6 ?

Pls explain what am I missing here.
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by ani781 » Mon Sep 02, 2013 6:46 am
Hi ,
I am little confused with the statement D.
Why is it not that n > 36^1/2 => n > +6 / -6.

Is not sqrt of 36 = +/- 6 ?

Pls explain what am I missing here.
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by Brent@GMATPrepNow » Mon Sep 02, 2013 6:50 am
ani781 wrote:Hi ,
I am little confused with the statement D.
Why is it not that n > 36^1/2 => n > +6 / -6.

Is not sqrt of 36 = +/- 6 ?

Pls explain what am I missing here.
No, √36 does not equal 6 and -6
√n denotes the positive number whose square is n.
So, √36 = 6 (and only 6)

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by ani781 » Mon Sep 02, 2013 7:18 am
Thanks Brent, but please elaborate a little more... Is not -6 * -6 = 36 ?
Is it then |sqrt 36| which gives +6 / -6 ?
Where lies the difference between them ?
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by Brent@GMATPrepNow » Mon Sep 02, 2013 8:14 am
ani781 wrote:Thanks Brent, but please elaborate a little more... Is not -6 * -6 = 36 ?
Is it then |sqrt 36| which gives +6 / -6 ?
Where lies the difference between them ?
This all has to do with agreed-upon notation. From the Official Guide:

A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3.

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by ani781 » Mon Sep 02, 2013 9:24 am
Thanks a lot Brent.... This was a piece I had overlooked ... could you kindly guide me to any such more assumptions if any... I would be grateful...

Best Regards.
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by Brent@GMATPrepNow » Mon Sep 02, 2013 10:00 am
ani781 wrote:Thanks a lot Brent.... This was a piece I had overlooked ... could you kindly guide me to any such more assumptions if any... I would be grateful...

Best Regards.
I can't think of any other assumptions regarding square roots.
I guess there's this fact: the square root of a negative number is not a real number.

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