q: Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
Options:
(A) 223
(B) 776
(C) 287
(D) 196
(E) 211
a: Stream of consciousness: Division of m+n+p objects into three groups is given by (m+n+p)!m!n!p!(m+n+p)!m!n!p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!3!3!12!(7)!1!3!3!12! + (7)!1!2!4!(7)!1!2!4! + (7)!1!1!5!12!(7)!1!1!5!12! = 70 + 105 + 21 = 196 The answer is (D).

question: A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
(A) 6
(B) 5
(C) 7
(D) 3
(E) 2
answer: Stream of consciousness: Speed downstream = d/t = 90/3 = 30 kmph
Speed upstream = d/t = 72/(3) = 24 kmph
The speed of the stream = (30 - 24)/2 = 3 kmph The answer is (D).

q: Which of the following numbers is divisible by 4?
Options:
(A) 27767
(B) 10224
(C) 26778
(D) 26679
(E) 26711
a: Stream of consciousness: 10224. This is the only option with last two digits divisible by 4 The answer is (B).

question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). The temperature required to boil liquid A and liquid B differed by 35 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
Options:
(A) a) 17
(B) b) 13
(C) c) 25
(D) d) 45
(E) e) 81
answer: Stream of consciousness: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick A which is the only number near half of 35. The other answer choices are too far apart so no need to calculate. The answer is (A).

q: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
(A) 288
(B) 270
(C) 287
(D) 209
(E) 271
a: Stream of consciousness: I = (500*9*6)/100 = 270 The answer is (B).

q: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 21
(B) 20
(C) 17
(D) 12
(E) 18
a:
Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 70 = 20 The answer is (B).