Data Sufficiency

Fab79 wrote:If r, s, and t are all positive, what is the ratio of r to s to t?

(1) r - s = 2s and (t - 2s)2 = 0
(2) r = 6 and t = 8s-1

I assume it would be (t - 2s)²

Statement 1: r - s = 2s ---> r = 3s
(t - 2s)² = 0 ---> (t - 2s) = 0 ---> t = 2s

So, the required ratio = r:s:t = 3s:s:2s = 3:1:2

Sufficient

Statement 2: From the given information we cannot uniquely determine the ratio of r to s to t.
For example, consider the following two cases,

• r = 6, s = 1, t = 7 ---> r:s:t = 6:1:7
  r = 6, s = 2, t = 15 ---> r:s:t = 6:2:15

Not sufficient

The correct answer is A.

[email protected] wrote:If whole square of (t-2s)=0, will t-s be also equal to zero?

No.
If square of any number is zero, then the number must be zero.
Here, (t - 2s)² = 0.
So, (t - 2s) must be equal to zero.
--> (t - 2s) = 0
--> t = 2s

But this in no way means (t - s) will be equal to zero.
For example,

• t = 2, s = 1 ---> (t - 2s) = 0 but (t - s) ≠ 0
  t = 4, s = 2 ---> (t - 2s) = 0 but (t - s) ≠ 0
  t = 6, s = 3 ---> (t - 2s) = 0 but (t - s) ≠ 0

Only when t = s = 0, then both (t - 2s) and (t - s) will be equal to zero, but in this case, t and s are positive. So, (t - s) is never equal to zero.

Hope that helps.