How many digits are in the number 50^8 8^3 11?
Options:
(A) 18
(B) 20
(C) 19
(D) 22
(E) 17
Answer and stream of consciousness: (A)
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 = (5^2*2)^8*2^9*11 = 5^16*2^17*11 = 2*11*10^16 = 22*10^16
Hence we would have 16 trailing 0's and the three digits from 22
Total digits = 2 + 16 = 18

How long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length?
Options:
(A) 16.5
(B) 16.0
(C) 16.4
(D) 14
(E) 16.1
Answer and stream of consciousness: (D)
Stream of consciousness: D = 110 + 170 = 280 m
S = 72 * 5/18 = 20
T = 280 * 1/20 = 14 sec

A shipment of 8 TV sets contains 4 black and white sets and 4 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
Options:
(A) 1/7
(B) 11/14
(C) 5/14
(D) 11/28
(E) 13/28
Answer and stream of consciousness: (B)
Stream of consciousness: 4/8 * 3/7 = 12/56
1-(12/56) = 44/56 = 11/14

The average of seven numbers is 21. The average of first three numbers is 19 and the average of last three numbers is 23. What is the middle number?
Options:
(A) 20
(B) 22
(C) 18
(D) 19
(E) 21
Answer and stream of consciousness:
(E)
Stream of consciousness: The total of seven numbers = 7X21 = 147
The total of first 3 and last 3 numbers is = 3 X 19+3 X 23 = 126
So, the middle number is (147 - 126 ) = 21