q: 100 white and black tiles will be used to form a 20x20 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
(A) 75
(B) 80
(C) 85
(D) 70
(E) 95
a: Stream of consciousness: Answer = D
Please refer diagram below
80 - 10 = 70 The answer is (D).


question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?
Options:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 0
answer: Stream of consciousness: A number ending with 2 can never be a perfect squar The answer is (E).


q: 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) 356
(B) 278
(C) 127
(D) 279
(E) 150
a: 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 (E).


question: A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue?
Options:
(A) 5/19
(B) 9/20
(C) 1/57
(D) 15/57
(E) 15/684
answer: Stream of consciousness: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57 The answer is (C).


q: Which of the following numbers is divisible by 9?
Options:
(A) 23274
(B) 25181
(C) 31001
(D) 50123
(E) 11251
a: Stream of consciousness: 23274. This is the only option with last two digits divisible by 9 The answer is (A).


q: The average of first six prime numbers greater than 20 is?
Options:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 34
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: 23 + 29 + 31 + 37 + 41 + 43 = 204/6 = 34 The answer is (E).