question: How many digits are in the number 50^8 8^3 11^2 x 10^2?
Options:
(A) 22
(B) 20
(C) 21
(D) 18
(E) 17
answer: Stream of consciousness: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 8^3 11^2 x 10^2 = (5^2*2)^8*2^9*11^2x 10^2 = 5^16*2^17*11^2 x10^2 = 2*11^2*10^16x10^2 = 242*10^18
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 18 = 21 The answer is (C).

q: In how many different ways can the letters of the word 'PREPTY' be arranged?
Options:
(A) 280
(B) 290
(C) 300
(D) 340
(E) 360
a: Stream of consciousness: Number of ways = 61/21 6X5X4X3X2X1 - 360 The answer is (E).

question: What is the sum of all the prime numbers greater than 30 but less than 50?
Options:
(A) 126
(B) 199
(C) 198
(D) 188
(E) 122
answer: Stream of consciousness: Required sum = (31 + 37 + 41 + 43 + 47) = 199
Note: 1 is not a prime number The answer is (B).

q: How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 28
(C) 29
(D) 11
(E) 12
a: Stream of consciousness: (60/100) * 50 (40/100) * 30
30 - 12 = 18 The answer is (A).

question: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?
Options:
(A) 54 sec
(B) 28 sec
(C) 25 sec
(D) 45 sec
(E) 24 sec
answer: Stream of consciousness: D = 100 + 180 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec The answer is (B).

question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 40
(B) 48
(C) 45
(D) 50
(E) 25
answer:
Stream of consciousness: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec The answer is (B).