q: If x<0, y>0, and |x| < |y|, which of the following must be true?
Options:
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) x < y
(E) x < y
a: Stream of consciousness: Correct Answer: (E)
Let's go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn't have to be true consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us x > y. Remember that x < 0, so x = |x|, and y is positive, so |y| = y. Thus x < y is the same statement as |x| > |y|, and (D) must be true. The answer is (D).

question: Find the average of the first 21 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
answer: Stream of consciousness: Average of the first 'n' natural numbers = (n + 1)/2
We get (21+ 1)/2 = 11 The answer is (D).

q: A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?
Options:
(A) 6
(B) 15
(C) 17
(D) 18
(E) 2
a: Stream of consciousness: Speed downstream = d/t = 120/(2 ) = 60 kmph
Speed upstream = d/t = 60/(2) = 30 kmph
The speed of the stream = (60 - 30)/2 = 15 kmph The answer is (B).

question: The inverse ratio of 3: 6: 1 is?
Options:
(A) 2:3:7
(B) 2:3:9
(C) 2:1:6
(D) 2:3:6
(E) 2:3:1
answer: Stream of consciousness: 1/3: 1/6: 1/1 = 2:1:6 The answer is (C).

q: The total number of apples and oranges in the refrigerator is 7 more than the total number of oranges and peaches in the refrigerator. How much lesser is the number of peaches in the refrigerator as compared to apples?
Options:
(A) 2
(B) 8
(C) 7
(D) 6
(E) 4
a: Stream of consciousness: (Apples + Oranges) - (Oranges + Peaches) = 7
Apples - Peaches = 7 The answer is (C).

q: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
a:
Stream of consciousness: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 The answer is (C).