q: What is the greatest positive integer x such that 4^x is a factor of 64^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a: Stream of consciousness: 64^10 = (4^3)^10 = 4^30 The answer is (E).

question: A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?
Options:
(A) 5/5
(B) 5/9
(C) 5/1
(D) 1/3
(E) 5/2
answer: Stream of consciousness: Total number of outcomes possible when a die is rolled, n(S) = 6 ( 1 or 2 or 3 or 4 or 5 or 6)
E = Event that the number shown in the dice is divisible by 3 = {3, 6}
The probability = 2/6 = 1/3. The answer is (D).

q: There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number?
Options:
(A) 5
(B) 7
(C) 11
(D) 13
(E) 15
a: Stream of consciousness: (385/1001) = 5/13 First Number is 5 The answer is (A).

question: A train 120 meters long completely crosses a 480 meters long bridge in 55 seconds. What is the speed of the train is?
Options:
(A) 32
(B) 545
(C) 39
(D) 40
(E) 09
answer: Stream of consciousness: S = (120 + 480)/45 = 600/55 * 18/5 = 39 The answer is (C).

q: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 65 sec
(B) 16 sec
(C) 87 sec
(D) 99 sec
(E) 96 sec
a: Stream of consciousness: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec The answer is (B).

q: John has $2500 in his bank account that earns 10% interest every year. How much will be in John's bank account after one year?
Options:
(A) $2600
(B) $3000
(C) $2250
(D) $2750
(E) $3500
a:
Stream of consciousness: Final number = Initial number + 20%(original number) = 2500 + 10%(2500) = 2500 + 250 = 2750. The answer is (D).