q: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
a: Stream of consciousness: A intersect B intersect C = 4
A intersect B but not C = 1
B intersect C but not A = 1
C intersec A but not B = 1
A only is 2; B only is 2; C only is 2
Therefore, total 13 members serve on one or more boards of directors. The answer is (B).

question: Let p be a prime number greater than 2 and let N = 14p. How many even numbers divide N?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
answer: Stream of consciousness: Answer: A. There is exactly one. The prime factorization of 14 is 14 = 2*7, so N = 2*7*p = 7*2*p = 7*2p, so 2p is the only even number that divides N. The answer is (A).

q: Find the mean proportional between 49 & 64?
Options:
(A) A) 59
(B) B) 61
(C) C) 56
(D) D) 65
(E) E) 67
a: Stream of consciousness: Formula = ab
A = 49 and B = 64
4964 = 7 8 = 56 The answer is (C).

question: If Ram rides his cycle in the speed of 18 km/hr from his office, in what time will he reach his house which is 900 m long from his office?
Options:
(A) 2
(B) 4
(C) 5
(D) 7
(E) 3
answer: Stream of consciousness: Speed = 18 * 5/18 = 5 m/sec
Time taken = 900/5 = 180 sec ie. 3 mins. The answer is (E).

q: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
Options:
(A) 5
(B) 7
(C) 23
(D) 4
(E) 2
a: Stream of consciousness: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. The answer is (A).

q: For integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?
Options:
(A) At least one of U and V is odd
(B) The sum U + V is odd
(C) U and V share no common factors other than 1
(D) UV is odd.
(E) U is odd
a:
Stream of consciousness: At least one of U and V is odd The answer is (A).