Q: There are 20 balls in a jar. You take out 2 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
Options:
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
A: OK... Stream of consciousness: 12 = 3 blue balls + 18 / 2
The answer is (A).

Q: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many ways can the test be completed if every question is unanswered?
Options:
(A) 24
(B) 120
(C) 625
(D) 720
(E) 1024
A: OK... Stream of consciousness: 5 choices for each of the 4 questions, thus total of 5*5*5*5 = 5^4 = 625 ways.
The answer is (C).

Q: From among the 39 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1482
(E) 1460
A: OK... Stream of consciousness: There are 39 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 39 ways. When one person is appointed as leader, we are left with 35 students. Out of these 38 teachers, we can select one class representative. So, a class representative can be selected in 38 ways. Hence, the number of ways in which a leader and class representative can be selected = 39 x 38 = 1482
The answer is (D).

Q: A can do a job in 20 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
Options:
(A) 22 1/6
(B) 24
(C) 22 1/0
(D) 22 1/9
(E) 22 1/1
A:

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
OK... Stream of consciousness: 1/20 + 1/30 = 5/60 = 1/12
12 = 12 *2 = 24 days
The answer is (B).