q: How many digits are in the number 50^8 8^3 11?
Options:
(A) 18
(B) 20
(C) 19
(D) 22
(E) 17
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 The answer is (A).

question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
Options:
(A) 1
(B) 3
(C) 5
(D) 8
(E) 9
answer: Stream of consciousness: If he draws any combination of 3 socks he will definitely have the matching pair of either colour. The answer is (A).

q: An design manager has 10patterns of chairs & 6patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 20
(B) 60
(C) 80
(D) 90
(E) 100
a: Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 6 ways
Hence one chair and one table can be arranged in 10 x 6 ways = 60 ways The answer is (B).

question: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 2356
(B) 3467
(C) 4567
(D) 5189
(E) 5184
answer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).

q: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
Options:
(A) 267
(B) 766
(C) 810
(D) 868
(E) 812
a: Stream of consciousness: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810 The answer is (C).

q: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 23 inches, how many inches of framing material does the carpenter need to frame the painting?
Options:
(A) 12
(B) 22 1/2
(C) 37 1/2
(D) 50
(E) 29
a:
Stream of consciousness: (23/2) ( 2+3) * 2 = 29 = The answer is (E).