The average of 7 consecutive numbers is 33. The highest of these numbers is:
Options:
(A) 28
(B) 30
(C) 33
(D) 36
(E) 28

The average of 7 consecutive numbers will be the 4th number which is given to be = 33 5th number = 34, 6th number = 35, 7th number = 36 So the answer is: (D).

A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds. What is the length of the platform in meters?
Options:
(A) 240 meters
(B) 360 meters
(C) 300 meters
(D) 600 meters
(E) Cannot be determined

Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 15 * 20 = 300 = Length of train
Length of platform = 600 - 300 = 300 So the answer is: (C).

A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 45 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17 minutes
(B) 87 minutes
(C) 36 minutes
(D) 27 minutes
(E) 11 minutes

1/20 - 1/45 = 1/36
36 minutes So the answer is: (C).

A bag contains 3 red and 2 black ball. Another bag contains 4 red and 5 black balls. A ball is drawn from the first bag and is placed in the second. A ball is then drawn from the second. What is the probability that this draw of red ball is due to the drawing of red ball from the first bag ?
Options:
(A) 3/5
(B) 2/5
(C) 4/25
(D) 3/10
(E) 15/23
Probability of getting red ball from bag1 and then red from bag 2 = 3/5*5/10 = 15/50
Probability of getting black ball from bag1 and then red from bag 2 = 2/5*4/10 = 8/50
Now comes the condition, hence apply conditional probability:
P(Red)/ P(Red + Black)
(15/50)/(15/50+8/50) = 15/50 /23/50 = 15/23. So the answer is: (E).