Square Root

[Benni]

Hi Guys,

regarding OG 13, 157, Data Suffiency.

If n is a positive integer and k=5.1x10^n, what is value of k?
(1) 6000<k<500 000
(2) k²=2.601x10^9

OA is D.


What I dont get is. k²=2.601x10^9. Therefore k=Plus or Minus Squareroot of 2.601x10^9. So in my view 2 is not sufficient. My question therefore is: When do I have to take account of the negative square root and when do I ignore it.

Thanks

[Brent@GMATPrepNow]

Hi Guys,

regarding OG 13, 157, Data Suffiency.

If n is a positive integer and k=5.1x10^n, what is value of k?
(1) 6000<k<500 000
(2) k²=2.601x10^9

OA is D.


What I dont get is. k²=2.601x10^9. Therefore k=Plus or Minus Squareroot of 2.601x10^9. So in my view 2 is not sufficient. My question therefore is: When do I have to take account of the negative square root and when do I ignore it.

Thanks

You're right to say that the equation k²=2.601x10^9 tells is that k = sqrt(2.601x10^9) or k = -sqrt(2.601x10^9).
However, the question also tells us that k=5.1x10^n. Since 5.1x10^n must always have a positive value, we know that k must be positive.
If k is positive, then k cannot equal -sqrt(2.601x10^9).
So, k must = sqrt(2.601x10^9)

Cheers,
Brent

[Benni]

Thank you for your very quick reply. I appreciate it. Your explaination is just fantastic.

But if you could please take a look at OG 13, 167, Datasufficiency:

If n and k are positive integers, is sqrt(n+k) > 2sqrt(n)?
1) k > 3n
2) n + k > 3n
OA is A.

They square the inequality to n+k>2n saying n and k are positive.
But what about following example: sqrt9>sqrt 4? --> solution one 3>2 and solution two -3>-2.
Now by squaring the solution b is lost. And this drives me crazy. Why are we allowed to square here.

Thank you very much.
Ben

[Brent@GMATPrepNow]

Thank you for your very quick reply. I appreciate it. Your explaination is just fantastic.

But if you could please take a look at OG 13, 167, Datasufficiency:

If n and k are positive integers, is sqrt(n+k) > 2sqrt(n)?
1) k > 3n
2) n + k > 3n
OA is A.

They square the inequality to n+k>2n saying n and k are positive.
But what about following example: sqrt9>sqrt 4? --> solution one 3>2 and solution two -3>-2.
Now by squaring the solution b is lost. And this drives me crazy. Why are we allowed to square here.

Thank you very much.
Ben

The problem is indicated above in blue.

The square root notation essentially asks us for the positive square root.
That is, sqrt(9) = 3 (but not -3)

A lot of students make the mistake of assuming that the equation x^2 = 9 is virtually identical to the equation x = sqrt(9). These two equations are not identical.

The equation x^2 = 9 has two solutions: x=3 and x=-3
The equation x = sqrt(9) has only one solution: x=3

Cheers,
Brent

[Benni]

Many thanks for your lovely explanation!.