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

question: In 2005, 25 percent of the math department's 40 students were female, and in 2007, 40 percent of the math department's 85 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Options:
(A) 15%
(B) 50%
(C) 62.5%
(D) 115%
(E) 240%
answer: Stream of consciousness: Female students in 2005 = 25% of 40 = 10
Female students in 2007 = 40% of 85 = 34
Percentage increase = [(34- 10)/10] *100 % = 240% The answer is (E).

q: Two pipes A and B can fill a cistern in 15 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
(A) 17 1/4 min
(B) 28 1/7 min
(C) 17 1/7 min
(D) 13 3/7 min
(E) 17 5/7 min
a: Stream of consciousness: 1/15 + 1/30 - 1/40 = 9/120
120/9 = 13 3/7 The answer is (D).

question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40 sec
(B) 22 sec
(C) 27 sec
(D) 17 sec
(E) 37 sec
answer: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec The answer is (A).

q: What is the greatest positive integer x such that 6^x is a factor of 216^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a: Stream of consciousness: 216^10 = (6^3)^10 = 6^30 The answer is (E).

q: An design manager has 10patterns of chairs & 7patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 70
(B) 40
(C) 80
(D) 90
(E) 100
a:
Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 7 ways
Hence one chair and one table can be arranged in 10 x 7 ways = 70 ways The answer is (A).