q: Fill in the blank with the correct number in this number series: 5, 15, 7, 12, __, 9, 11,... ?
Options:
(A) 6
(B) 9
(C) 8
(D) 7
(E) 5
a: Stream of consciousness: In this simple alternating subtraction and addition series; The first series begins with 5 and adds 2; the second begins with 15 and subtracts 3, and so on. The answer is (B).


question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
(A) 25 kmph
(B) 32 kmph
(C) 40 kmph
(D) 38 kmph
(E) 92 kmph
answer: Stream of consciousness: S = (100 + 300)/45 = 400/45 * 18/5 = 32 kmph The answer is (B).


q: The average mark obtained by 22 candidates in an examination is 48. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
Options:
(A) 22
(B) 0
(C) 49
(D) 58
(E) 66
a: Stream of consciousness: It is clear that 22 x 48 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 66 The answer is (E).


question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2354
(B) 2644
(C) 2645
(D) 4577
(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: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
(A) 180
(B) 19
(C) 60
(D) 12
(E) 720
a: Stream of consciousness: 5C3 * 4C2 * 3C2 = 10*6*3 = 180. The answer is (A).


q: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be odd, how many different codes can be created?
Options:
(A) 20
(B) 22
(C) 24
(D) 1
(E) 30
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: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 555 will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 26 = 1. The answer is (D).