q: On a clock, how many times a day do the minute and hour hand overlap?
Options:
(A) 10
(B) 11
(C) 20
(D) 22
(E) 24
a: Stream of consciousness: 22 times: 12:00:00, 1:05:27, 2:10:55, 3:16:22, 4:21:49, 5:27:16, 6:32:44, 7:38:11, 8:43:38, 9:49:05, 10:54:33. Each twice a day. The answer is (D).


question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination. How many miles did John drive?
Options:
(A) 235 miles.
(B) 245 miles.
(C) 225 miles.
(D) 265 miles.
(E) 275 miles.
answer: Stream of consciousness: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 45 = 225 miles. The answer is (C).


q: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
Options:
(A) 99
(B) 98
(C) 97
(D) 96 answer
(E) 95
a: Stream of consciousness: The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this. The answer is (D).


question: Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
(A) Rs.1056
(B) Rs.1001
(C) Rs.2056
(D) Rs.1026
(E) Rs.1856
answer: Stream of consciousness: (900*3*3)/100 = 81
920 + 81 = 1001 The answer is (B).


q: A faucet, partially on, fills a bucket with water at a rate of r buckets per minute. If the faucet is turned up it will fill the same bucket at a rate r + 2 buckets per minute, and the same bucket would fill in 2/3 minute less. What is the value of r?
Options:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
a: Stream of consciousness: Equation: 1/r = 1/(r + 2) + 2/3
Plug options into the equation:
E fits: 1/1 = 1/(1 + 2) + 2/3 The answer is (E).


q: In a bucket there are 3 green balls and 2 yellow balls. What is the probability of drawing at least one green ball when drawing two consecutive balls randomly?
Options:
(A) 16/20
(B) 9/10
(C) 2/5
(D) 3/5
(E) ½
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
Stream of consciousness: P(at least one green) = 1 - P(no green, so 2 yellow) = 1- 2/5*1/4 = 9/10. The answer is (B).