q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 23
(B) 27
(C) 28
(D) 29
(E) 31
a: Stream of consciousness: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27 The answer is (B).


question: Which of the following numbers is divisible by 5?
Options:
(A) 3221
(B) 6175
(C) 6231
(D) 5813
(E) 4251
answer: Stream of consciousness: 6175. This is the only option with last two digits divisible by 5 The answer is (B).


q: A Train requires 10 seconds to pass a pole while it requires 40 seconds to cross a stationary train which is 300 mtrs long. Find the speed of the train.
Options:
(A) 36kmph
(B) 42kmph
(C) 48kmph
(D) 52kmph
(E) 64kmph
a: Stream of consciousness: In 10s the train crosses the pole and in 40 sec the train crosses one more stationary train
In 30 sec the train travels a distance of 300 mtrs
Speed = 300/30 = 10 m/s = 10 * 18/5 = 36 kmph The answer is (A).


question: How many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
(A) 28 sec
(B) 23 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
answer: Stream of consciousness: D = 130 + 150 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec The answer is (A).


q: An analyst will recommend a combination of 4 industrial stocks, 3 transportation stocks, and 4 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 5 utility stocks, how many different combinations of 11 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 100
(E) 720
a: Stream of consciousness: 5C4 * 4C3 * 5C4 = 5*4*5 = 100. The answer is (D).


q: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 6 industrial stocks, 5 transportation stocks, and 4 utility stocks, how many different combinations of 6 stocks are possible?
Options:
(A) 1200
(B) 900
(C) 600
(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 * 5C2 * 4C2 = 15*10*6 = 900. The answer is (C).