HSPA wrote:If r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1, is w < 70?
(1) r > 0.5
(2) r > s

(1) r > 0.5
Let us take r = 0.6. Then s = 0.4 (as r + s = 1). So, w = 60r + 80s = 60(0.6) + 80(0.4) = 68, which is less than 70.
If we take r = 0.5. Then s = 0.5 (as r + s = 1). So, w = 60r + 80s = 60(0.5) + 80(0.5) = 70.
So, the answer to the main question is "yes".
Hence, (1) is SUFFICIENT.

(2) r > s implies that r should always be greater than 0.5 (as r + s = 1), which is the same as (1).
Hence, (2) is SUFFICIENT.

The correct answer is D.

If r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1, is w < 70?
(1) r > 0.5
(2) r > s

One can also approach this algebraically. If r + s = 1, then s = 1 - r, so by substitution, w = 60r + 80(1 - r) = 60r + 80 - 80r = 80 - 20r.

Now if w = 80 - 20r, then if r > 0.5, then 20r > 10, so w will certainly be less than 70. Similarly, if r > s and r+s=1, then r > 0.5, so Statement 2 gives the same information as Statement 1, and each Statement is sufficient alone.

Still, I also find it fastest to look at this as a weighted average question, as a couple of people have done above. There's a similar (official) question at the link below - one which on the surface looks like an abstract algebra problem, but which is fundamentally based on weighted averages:

https://www.beatthegmat.com/tough-algebr ... 13568.html