What is the are of an equilateral triangle of side 18 cm?
Options:
(A) 663 cm2
(B) 743 cm2
(C) 813 cm2
(D) 645 cm2
(E) 143 cm2

Area of an equilateral triangle = 3/4 S2
If S = 18, Area of triangle = 3/4 * 18 * 18 = 813 cm2; So the answer is: (C).

The average of 13 result is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?
Options:
(A) 35
(B) 37
(C) 46
(D) 48
(E) 50

Sum of all the 13 results = 13 * 60 = 780
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 - 780 = 46. So the answer is: (C).

A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue?
Options:
(A) 5/19
(B) 9/20
(C) 1/57
(D) 15/57
(E) 15/684

It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57 So the answer is: (C).

If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 288
(B) 162
(C) 878
(D) 168
(E) 122
12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km. So the answer is: (B).