q: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
Options:
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
a: Stream of consciousness: If the number is divisible by 9, it must also be divisible by 3. Only 7 yields such a number. The answer is (D).

question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/3
(C) 1/5
(D) 1/1
(E) 1/2
answer: 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).

q: What is the are of an equilateral triangle of side 12 cm?
Options:
(A) 363 cm2
(B) 743 cm2
(C) 643 cm2
(D) 645 cm2
(E) 143 cm2
a: Stream of consciousness: Area of an equilateral triangle = 3/4 S2
If S = 12, Area of triangle = 3/4 * 12 * 12 = 363 cm2; The answer is (A).

question: Last year, Company X made q dollars in profit. Half of the profit went to the company's founder. The rest was split evenly among his Five other partners. In terms of q, how much did each of the other partners receive?
Options:
(A) q/12
(B) q/5
(C) q/10
(D) q/7
(E) q/8
answer: Stream of consciousness: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 5
Profit to each partner = (q/2)/5 = q/10 The answer is (C).

q: A train running at the speed of 90 km/hr crosses a pole in 12 seconds. Find the length of the train?
Options:
(A) 150
(B) 872
(C) 287
(D) 288
(E) 300
a: Stream of consciousness: Speed = 90*(5/18) m/sec = 75/3 m/sec
Length of Train (Distance) = Speed * Time
(75/3) * 12 = 300 meter The answer is (E).

q: Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2?
Options:
(A) x^2
(B) x^2+1
(C) x^2 +4
(D) x^2+2x
(E) x^2+4x
a:
Stream of consciousness: Avg = [(x+1)^2 + (x-1)^2] / 2
Expanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1 The answer is (B).