question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 65 with him, what was the average amount with the group before his joining the group?
Options:
(A) s. 25.6
(B) s. 145/6
(C) s. 16.6
(D) s. 26
(E) s. 25
answer: Stream of consciousness: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 50. So, the amount with remaining 6 people = 210 - 65 = Rs. 145
The average amount with them = 145/6 The answer is (B).
--
question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Options:
(A) 165
(B) 185
(C) 205
(D) 225
(E) 245
answer: Stream of consciousness: Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = C = C = (11 * 10 * 9)/(3 * 2) = 165 ways. The answer is (A).
--
question: In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 48
(B) 1720
(C) 2880
(D) 5040
(E) 10080
answer: Stream of consciousness: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48. The answer is (A).
--
question: The average age of applicants for a new job is 32, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
Options:
(A) 8
(B) 77
(C) 7
(D) 18
(E) 34
answer:
Stream of consciousness: Minimum age = Average - 1 Standard deviation = 32 - 8 = 24
Maximum age = average + 1 Standard deviation = 32+ 8 = 40
Maximum number of different ages of the applicants = 30 - 24 + 1 = 7 The answer is (C).
--