Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = C/C = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
The answer: (B)
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
(A) 92/37
(B) 33/91
(C) 71/28
(D) 91/42
(E) 91/33
Reasoning: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 96
11K = 96 * 4 +1 = 384 +1 = 385
K = 385 / 11 = 35.
Ans: (D)
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K 5 and 5K + 1 is 96, what is the value of K?
Options:
(A) 11
(B) 15 3/4
(C) 22
(D) 35
(E) 25 3/10
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
The answer: (A)
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
Options:
(A) 1
(B) 3
(C) 5
(D) 8
(E) 9
Reasoning: The ratio is 2:3 = gym:ride, so (14)(3/2) = 21 minutes at the gym, and 21 + 14 = 35 minutes exercise, so (2/3)(35) = 23 minutes yoga.
Ans: (D)
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 14 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
(A) 10 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.
Rationale: E 87 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 87 matches were played.
The answer: (E)
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 88 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
Rationale: Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence
The answer: (C)
Question: There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
Options:
(A) 15
(B) 30
(C) 120
(D) 240
(E) 256