q: 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
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 × 11^2 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).


question: The average age of A, B and C is 29 years. If the average age of A and C is 32 years, what is the age of B in years ?
Options:
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23
answer: Stream of consciousness: Age of B = Age of (A + B + C) â€“ Age of (A + C) = 29 Ã— 3 â€“ 32 Ã— 2 = 87 â€“ 64 = 23 years The answer is (E).


q: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
Options:
(A) 2
(B) 3
(C) 5
(D) 4
(E) 9
a: Stream of consciousness: Integer is divisible by 3 - Sum of digits is divisible by 3 The answer is (D).


question: Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is four miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
Options:
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
answer: Stream of consciousness: It's a simple geometry problem. Look at the diagram below: The answer is (A).


q: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2567
(B) 3589
(C) 3789
(D) 4890
(E) 5184
a: 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: An analyst will recommend a combination of 2 industrial stocks, 3 transportation stocks, and 3 utility stocks. If the analyst can choose from 6 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 9 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: 6C2 * 3C3 * 4C3 = 15*1*4 = 60. The answer is (C).