question: In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?
Options:
(A) $9 x 10^4
(B) $9.90 x 10^6
(C) $1.00 x 10^7
(D) $1.05 x 10^7
(E) $9.90 x 10^7
answer: Stream of consciousness: The max product of any two balls can be 9 * 10 = 9900 = 9 * 10
If we multiply it by $1000 the max amount will be 9 * 10^4. The answer is (A).

q: Which among the following is the greatest?
Options:
(A) 2^3^2
(B) 2^2^3
(C) 3^2^3
(D) 3^3^3
(E) 5^3^3
a: Stream of consciousness: 2^3^2 = 29
2^2^3 = 28
3^2^3 = 38
3^3^3 = 327
As 327 > 38, 29 > 28 and 327 > 29. Hence 327 is the greatest among the four. The answer is (D).

question: What least number must be added to the least number of six digits so that the resulting number may be a perfect square.
Options:
(A) 489
(B) 267
(C) 278
(D) 199
(E) 111
answer: Stream of consciousness: The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 489 Least number to be added = 489. The answer is (A).

q: If a man walks to his office at 3/4 of his usual rate, he reaches office 1/3 of an hour later than usual. What is his usual time to reach office.
Options:
(A) 12 hr
(B) 1 hr
(C) 34 hr
(D) 2 hrs
(E) None of these
a: Stream of consciousness: If new speed is ab of original speed, then usual time (ba - 1) = change in time
usual time (43 - 1) = 13
usual time = 13 3 = 1 hr The answer is (B).

question: How long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length?
Options:
(A) 70 sec
(B) 60sec
(C) 82 sec
(D) 75 sec
(E) 62 sec
answer: Stream of consciousness: D = 1400+100 = 1500 m
S = 72 * 5/18 = 20
T = 1500 * 1/20 = 75 sec The answer is (D).

question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 20 sec
(E) 25 sec
answer:
Stream of consciousness: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec The answer is (D).