Q: Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
Options:
(A) 1
(B) 3
(C) 4
(D) 0
(E) 2
A: OK... Stream of consciousness: 4 points are possible in which 1 point is the incentre of the circle and other 3 are excentres
The answer is (C).

Q: A small company employs 3 men and 4 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
Options:
(A) 1/14
(B) 1/7
(C) 20/70
(D) 18/70
(E) 1/2
A: OK... Stream of consciousness: Total ways to choose 4 employees from 8 employees = 8C4
Two women = 4C2
Two Men = 3C2
P = (5C2 * 3C2)/8C2 = 18/70 hence
The answer is (D).

Q: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 56 ounces of this substance?
Options:
(A) 27
(B) 36
(C) 42
(D) 24
(E) 147
A: OK... Stream of consciousness: 112 ounces of a substance has a volume of 48 cubic inches
56 ounces of a substance has a volume of (48/112)*56 = 24 cubic inches
The answer is (D).

Q: The average of 13 numbers is 59. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 59
(B) 83
(C) 45
(D) 53
(E) 64
A:
OK... Stream of consciousness: Sum of all the 13 numbers = 13 * 59 = 767
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 767 = 59.
The answer is (A).