question: For some integer x, x^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 41
(B) 38
(C) 29
(D) 31
(E) 30
answer: Stream of consciousness: Hint: x^2-5 (x is an integer) is never multiple of 3 (try to prove this), hence 30 is out. The answer is (E).

q: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 25, and 30 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
Options:
(A) 4/11
(B) 1/2
(C) 15/22
(D) 150/11
(E) 11/4
a: Stream of consciousness: P1 takes 12 hrs
Rate for P2P3 together = 1/25 + 1/30 = 11/150
Therefore they take 150/11
Ratio = 150/11 = The answer is (D).

question: In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
Options:
(A) 10
(B) 12
(C) 30
(D) 40
(E) 20
answer: Stream of consciousness: Dist = (100/45*9) = 20 m The answer is (E).

q: A marble shop contains 6 blue marbles, 6 red marbles, and 6 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be the same color?
Options:
(A) 1/68
(B) 60/68
(C) 13/68
(D) 13/48
(E) 1/48
a: Stream of consciousness: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 1
Probability of choosing 2nd card of the same type: 5/17
Probability of choosing 3rd card of the same type: 4/16
Probability of choosing 4th marble of the same type: 3/15
Multiply and you get 1/68 The answer is (A).

question: Find the average of the first 23 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
answer: Stream of consciousness: Average of the first 'n' natural numbers = (n + 1)/2
We get (23 + 1)/2 = 12 The answer is (E).

question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
Options:
(A) 22 1/6
(B) 22 1/2
(C) 22 1/0
(D) 22 1/9
(E) 22 1/1
answer:
Stream of consciousness: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 1/4 *2 = 22 1/2 days The answer is (B).