q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 16. What is the middle number?
Options:
(A) 27
(B) 29
(C) 36
(D) 34
(E) 35
a: OK... The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 16 = 90
So, the middle number is (126 - 90 ) = 36
The answer is (C).

q: The average of five numbers is 18. The average of first two numbers is 14 and the average of last two numbers is 19. What is the middle number?
Options:
(A) 24
(B) 27
(C) 29
(D) 32
(E) 34
a: OK... The total of seven numbers = 5X18 = 90
The total of first 2 and last 2 numbers is = 2 X 14+2 X 19 = 66
So, the middle number is (90 - 66 ) = 24
The answer is (A).

q: The average of seven numbers is 18. The average of first three numbers is 12 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 25
(B) 27
(C) 29
(D) 33
(E) 34
a:
OK... The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 12+3 X 19 = 99
So, the middle number is (126 - 93 ) = 33
The answer is (D).