q: The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 72
(B) 83
(C) 45
(D) 53
(E) 64
a: OK... Sum of all the 13 numbers = 13 * 58 = 754
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 - 754 = 72.
The answer is (A).

q: If a man can cover 24 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 118 km
(B) 162 km
(C) 324 km
(D) 1887 km
(E) 177 km
a: OK... 24 m/s = 24 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 24 * 18/5 * 15/4 km = 324 km.
The answer is (C).

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