(Ans). (A)
(Question). The average of seven numbers is 15. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 6
(B) 29
(C) 31
(D) 34
(E) 35
(CoT). The total of seven numbers = 7X15 = 105
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (105 - 99 ) = 6


(Ans). (A)
(Question). In an office, 10 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Options:
(A)  16
(B)  64
(C)  50
(D)  144
(E)  160
(CoT). (10/100)Workers = 16 = > number of workers = 160
(10/100)*Workers = x+16 = > x = 16


(Ans). (D)
(Question). A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 4.5 km long?
Options:
(A) 4
(B) 3
(C) 5
(D) 6
(E) 9
(CoT). D = 25 * 60 + 4500 = 6000 m
T = 6000/60 * 18/5 = 360 sec = 6 mins


(Ans). (A)
(Question).

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
The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
(A) 9
(B) 8
(C) 7
(D) 6
(E) 2
(CoT). 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9