question: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 2234
(B) 4350
(C) 4560
(D) 5132
(E) y=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: A train 250 m long running at 72 kmph crosses a platform in 40 sec. What is the length of the platform?
Options:
(A) 450m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m
a: Stream of consciousness: D = 72 * 5/18 = 40 = 800 250 = 450m The answer is (A).

question: If 12x = 16y = 28z, then what is a possible sum of positive integers x, y, and z?
Options:
(A) 52
(B) 58
(C) 122
(D) 84
(E) 168
answer: Stream of consciousness: 12x = 16y = 28z
3x = 4y = 7z
3(4*7) = 4(3*7) = 7(3*4)
Addition = 28+21+12 = 61
Answer would be multiple of 61 which is 122 The answer is (C).

q: The average age of a family of 6 members is 26 years.If the age of the youngest member is 10 years,what was the average age of the family at the birth of the youngest member?
Options:
(A) 15
(B) 18
(C) 16
(D) 12
(E) 19
a: Stream of consciousness: Present age of total members = 6 X 26 = 156
10 yrs back their ages were = 6 x 10 = 60
Ages at the birth of youngest member = 156 - 60 = 96
Therefore, avg age at the birth of youngest member = 96/6 = 16. The answer is (C).

question: Find the remainder when 6^23 is divided by 5 ?
Options:
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
answer: Stream of consciousness: 6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216
216/5 remainder = 1 The answer is (C).

question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds. What is the length of the platform in meters?
Options:
(A) 240 meters
(B) 260 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
answer:
Stream of consciousness: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 17 * 20 = 340 = Length of train
Length of platform = 600 - 340 = 260 The answer is (B).