q: There are 8 books in a shelf that consist of 1 paperback books and 7 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) 21
(B) 45
(C) 50
(D) 55
(E) 60
a: Stream of consciousness: 8C3 [Select any four] - 7C3 [Select all hard backs] = 21 The answer is (A).

question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
(A) 35
(B) 45
(C) 50
(D) 55
(E) 60
answer: Stream of consciousness: 8C4 [Select any four] - 7C4 [Select all hard backs] = 35. The answer is (A).

q: Which of the following numbers is divisible by 12?
Options:
(A) 1332
(B) 1021
(C) 3221
(D) 4211
(E) 3233
a: Stream of consciousness: 1332. This is the only option with last two digits divisible by 12 The answer is (A).

question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
answer: Stream of consciousness: 5C3 * 4C2 * 3C2 = 10*6*3 = 180. The answer is (D).

q: The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 27
(B) 29
(C) 31
(D) 41
(E) 35
a: Stream of consciousness: The total of seven numbers = 7X20 = 140
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (140 - 99 ) = 41 The answer is (D).

q: What should come in place of the question mark (?) in the following equation?
12400 + 6899 = 610+ ?
Options:
(A) 12345
(B) 56894
(C) 18689
(D) 23478
(E) 94561
a:
Stream of consciousness: 12400 + 6899 = 610+ ?
12400 + 6899 610 = 18689 The answer is (C).