question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?
Options:
(A) 5/15
(B) 5/12
(C) 5/19
(D) 5/12
(E) 5/11
answer: Stream of consciousness: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12 The answer is (B).


q: 5,9,19,31,51,__
Options:
(A) 84
(B) 80
(C) 81
(D) 82
(E) 83
a: Stream of consciousness: (9+5) +5 = 19
(16+9) +6 = 31
(28+16)+7 = 51
(48+28)+8 = 84 The answer is (A).


question: The average age of a family of 6 members is 40 years.If the age of the youngest member is 7 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 33
(B) 18
(C) 21
(D) 12
(E) 19
answer: Stream of consciousness: Present age of total members = 6 X 40 = 240
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 240 - 42 = 198
Therefore, avg age at the birth of youngest member = 198/6 = 33. The answer is (A).


q: A certain league has three divisions. The respective divisions had 10, 12 and 15 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
(A)  70
(B)  72
(C)  73
(D)  78
(E)  80
a: Stream of consciousness: Overall, there can be 73 minuses. Tus, it is The answer is (C).


question: A 49 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 12
(B) 20
(C) 88
(D) 77
(E) 14
answer: Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 49 = 14 The answer is (E).


question: At a meeting of the 3 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 3 Chiefs of Staff be seated around a circular table?
Options:
(A) 120
(B) 480
(C) 960
(D) 2520
(E) 5040
answer:

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
Stream of consciousness: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer C (960), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect? The answer is (C).