question: Divide Rs.32000 in the ratio 3:7?
Options:
(A) 12000, 20000
(B) 9600, 22400
(C) 12000, 20007
(D) 12000, 20006
(E) 12000, 20001
answer: Stream of consciousness: 3/10 * 32000 = 9600
7/8 * 32000 = 22400 The answer is (B).


q: One copy machine can make 30 copies a minute, and a second copy machine makes 20 copies a minute. If the two copiers work together, how long would it take them to make 2,000 copies?
Options:
(A) 20 minutes
(B) 40 minutes
(C) 45 minutes
(D) 50 minutes
(E) 55 minutes
a: Stream of consciousness: Total work done by both machines in a minute = 30 + 20 = 50 copies
Total number of copies required = 2000
Time = 2000/50 = 40 mins The answer is (B).


question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 99 Θ (33 Θ 17)) ?
Options:
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
answer: Stream of consciousness: (( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 99 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
7 - 3 = 4. The answer is (D).


q: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 91 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
a: Stream of consciousness: A 90 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 90 matches were played. The answer is (A).


question: Count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5?
Options:
(A) Two
(B) Five
(C) Six
(D) Four
(E) One
answer: Stream of consciousness: Answer = A) Two
Numbers between 10 - 99 giving remainder 3 when divided by 9 = 12, 21, 30, 39, 48, 57, 66, 75, 84, 93
The Numbers giving remainder 2 when divided by 5 = 12, 57 = 2 The answer is (A).


question: Twenty coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^19
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
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: Fix the third coin as H. The remaining 19 coins have 2^19 outcomes. The answer is (A).