question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 650?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
answer: Stream of consciousness: 650 = 2*222 + (22*9) + 4*2
K weight of 600 = 2 +9+2 = 13 The answer is (D).


q: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
Options:
(A) 277
(B) 810
(C) 888
(D) 166
(E) 199
a: Stream of consciousness: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810 The answer is (C).


question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
(A) 118
(B) 150
(C) 277
(D) 258
(E) 191
answer: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m The answer is (B).


q: Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.
Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.1
What are the numbers?
Options:
(A) 1-2
(B) 1-3
(C) 2-4
(D) 3-4
(E) 2-3
a: Stream of consciousness: Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria. The answer is (D).


question: The distance between West-Town to East-Town is 14 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 2 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
Options:
(A) 3.
(B) 7.
(C) 10.
(D) 12.
(E) 15.
answer: Stream of consciousness: Time taken by the birds to meet = 14/(5+ 2) = 2 mins
Distance traveled by the bird traveling from West-Town = 5 * 2 = 10 The answer is (C).


question: a contract was signed to complete a job in 30 days. after how many days can 5 men leave then so that the job can be completed in 35 days
Options:
(A) 30 days.
(B) 35 days.
(C) 45 days.
(D) 55 days.
(E) 65 days.
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: If no of men used initially is x, then after (35-x) days 5 men can leave so that the job can be completed in 35 days. The answer is (B).