q: Simple interest on a certain sum is 16 over 25 of the sum. Find the rate per cent and time, if both are equal.
Options:
(A) 8% and 8 years
(B) 6% and 6 years
(C) 10% and 10 years
(D) 12 % and 12 years
(E) None of these
a: Stream of consciousness: 1625P = PRR/100
R2 = 160025 R = 405 = 8%
Also, time = 8 years The answer is (A).

question: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men?
Options:
(A) 5/7
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
answer: Stream of consciousness: Total ways to choose 4 employees from 8 employees = 8C3
Two men = 5C2
Two women = 3C1
P = (5C2 * 3C1)/8C2 = 5/7 hence The answer is (A).

q: A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event
'the number appearing is even' then find whether G and H are independent ?
Options:
(A) G and H are not independent events.
(B) G and H are independent events.
(C) Only G independent event
(D) Only H independent event
(E) None
a: Stream of consciousness: We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}
Then P(G) = 2/6 = 1/3
P(H) = 3/6 = 1/2 and P(G H) = 1/6
P(G n H) = P(G). P (H)
G and H are independent events. The answer is (B).

question: What is the are of an equilateral triangle of side 2 cm?
Options:
(A) 3
(B) 649
(C) 644
(D) 643
(E) 642
answer: Stream of consciousness: Area of an equilateral triangle = 3/4 S2
If S = 2, Area of triangle = 3/4 * 2 * 2 = 3 cm2; The answer is (A).

q: The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
a: Stream of consciousness: Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence The answer is (D).

q: How much 60% of 50 is greater than 30% of 30?
Options:
(A) 21
(B) 91
(C) 11
(D) 17
(E) 12
a:
Stream of consciousness: (60/100) * 50 (30/100) * 30
30 - 9 = 21 The answer is (A).