[Ques]: Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
(A) 4
(B) 8
(C) 12
(D) 14
(E) 16
*Ans*: (D)
--CoT--: The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.

[Ques]: For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.
Options:
(A) 10
(B) 5
(C) 2
(D) 3
(E) 1
*Ans*: (C)
--CoT--: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%

[Ques]: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 5 kmph
(B) 7 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
*Ans*: (D)
--CoT--: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph

[Ques]: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
(A) 150m
(B) 200m
(C) 250m
(D) 750m
(E) 300 m
*Ans*: (D)

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
--CoT--: D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m