question: How many positive integers less than 70 have a reminder 01 when divided by 3?
Options:
(A) 13
(B) 24
(C) 35
(D) 16
(E) 17
answer: Stream of consciousness: 1 also gives the remainder of 1 when divided by 3. So, there are total of 24 numbers. The answer is (B).


q: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
(A) 15 hours
(B) 14 hours
(C) 12 hours
(D) 74 hours
(E) 79 hours
a: Stream of consciousness: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work. The answer is (C).


question: There are 4 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?
Options:
(A) 10
(B) 8
(C) 40
(D) 60
(E) 120
answer: Stream of consciousness: Each person is one participant of 4 games. So there are in all 4*4 = 16 instances of one participant games. But each game has 2 participants so total number of games = 16/2 = 8 The answer is (B).


q: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 600 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
(A) 438
(B) 446
(C) 452
(D) 462
(E) 470
a: Stream of consciousness: Number of newborns that can die in first month = 1/10 *600 = 60
Survived = 540
Number of newborns that can die in second month = 1/10 * 540 = 54
Survived = 486
Number of newborns that can die in third month = 1/10 * 486 = 48
Survived = 438 The answer is (A).


question: The edge of a cube is 3a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 54a2
(E) 24a7
answer: Stream of consciousness: 6a2 = 6 * 3a * 3a = 54a2 The answer is (D).


question: John makes $50 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?
Options:
(A) 16%
(B) 16.66%
(C) 18%
(D) 21%
(E) 40%
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: Increase = (20/50)*100 = 40%. The answer is (E).