question: P and Q invested in a shop. The profits were divided in the ratio of 2 : 4 respectively. If P invested Rs. 500000, the amount invested by Q is:
Options:
(A) 5000000
(B) 4000000
(C) 1000000
(D) 6000000
(E) None
answer: Stream of consciousness: Suppose Q invested Rs. y. Then, 500000/y = 2/4 or y = [500000 x 4 / 2] = 1000000. The answer is (C).

q: In a school of 400 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
(A) 41
(B) 63
(C) 72
(D) 63
(E) 50
a: Stream of consciousness: 44 + 28 + 10 = 82%
100 82 = 18%
400 * 18/100 = 72 The answer is (C).

question: A motorcyclist goes from Bombay to Pune, a distance of 256 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 hours after the first, and reaches Pune hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 1:2
(B) 1:5
(C) 1:4
(D) 1:1
(E) 5:8
answer: Stream of consciousness: T = 256/32 = 8 h
T = 8 - 3 = 5
Time Ratio = 8:5
Speed Ratio = 5:8 The answer is (E).

q: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 2234
(B) 4350
(C) 4560
(D) 5132
(E) 5184
a: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).

question: Four of the five parts numbered as (a), (b), (c), (d) and (e)in the following equations are exactly equal. You have to find out the part that is not equal to the other parts. The number of that part is the answer.
Options:
(A) a2 + 5ab + 6b2
(B) (a + 3b) (a + 2b)
(C) a(a + 3b) + 2b(a + 3b)
(D) (3a + b) (a + 2b)
(E) a(a + 2b) + 3b(a + 2b)
answer: Stream of consciousness: The other parts are equal to a2 + 5ab + 6b2. The answer is (D).

question: For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.
Options:
(A) 10
(B) 5
(C) 2
(D) 3
(E) 1
answer:
Stream of consciousness: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50% The answer is (C).