Data Sufficiency

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

Cheers,
Brent

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.

GMAT assassins aren't born, they're made,
Rich

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

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)

Cheers,
Brent

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.

Cheers,
Brent

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.

Cheers,
Brent