the way i saw this this was noticed the term -2(s - 4)^2 is always negative, and only 0 when s = 4. which means the largest value of that term = 0 when s = 4. 32 is of course constant so the P(s) function achieves its maximum at s = 4. just different wording than above, but through a different lens.

thanks for the reply!

here's my take at it: to find P(jim wins), lets figure out all of his winning situations: (1) Jim chooses rock; renee chooses scissors (note their decisions are independent) (2) Jim chooses paper, renee chooses rock (3) Jim chooses scissors, renee chooses paper So P(Jim wins) = P(1) + P(2) + P(3). t...

i agree with neoreaves. just to clear up, we want to find: P(roar or rain) = P(roar) + P(rain) - P(roar AND rain) (1) makes P(roar AND rain) = 0, but we still need to find P(roar) + P(rain) (2) gives us a relationship between roars and rain, but we still need to find at least one of those unknowns t...

i agree with the above posts. E is the right answer and here's why: once you derive x+y < 73/72, it becomes clear you can come up with two numbers that are either < 1 (i.e. negative numbers for both x and y) or a pair of numbers whose sum is greater than 1 AND less than 73/72 (i.e. 729/720). gg gl

idiom: discouraged from

The idiom"discouraged from" appears on a bunch of lists of idioms used on the GMAT.

However, when is it correctly used, and when should you use "discouraged by"?

Thanks!