question: In how many different number of ways 6 men and 3 women can sit on a shopa which can accommodate persons?
Options:
(A) 200
(B) 230
(C) 504
(D) 250
(E) 260
answer: Stream of consciousness: 9p3 = 9 Ã— 8 Ã— 7 = 504 The answer is (C).


q: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
(A) 36
(B) 45
(C) 50
(D) 55
(E) 60
a: Stream of consciousness: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36. The answer is (A).


question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
Options:
(A) 1/6
(B) 1/7
(C) 1/5
(D) 1/9
(E) 1/2
answer: Stream of consciousness: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5 The answer is (C).


q: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 120, 30, 240, 25, ___, 20, 480, 15... Which number is missing?
Options:
(A) 120
(B) 360
(C) 340
(D) 960
(E) 280
a: Stream of consciousness: B 360
This is an alternating addition and subtraction series. In the first pattern, 120 is added to each number to arrive at the next. In the second, 5 is subtracted from each number to arrive at the next. The answer is (B).


question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
Options:
(A) 287
(B) 699
(C) 677
(D) 300
(E) 150
answer: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 300 m The answer is (D).


question: Solve:-
444 x 444 x 444 + 555 x 555 x 555 = ?(444 x 444 - 444 x 555 + 555 x 555)
Options:
(A) 888
(B) 333
(C) 999
(D) 988
(E) 889
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: Given Exp. = (a3 + b3) = (a + b) = (444 + 555) = 999(a2 - ab + b2) The answer is (C).