Ques: The average of thirteen numbers is 9. The average of first six numbers is 5 and the average of last six numbers is 7. What is the middle number?
Options:
(A) 47
(B) 45
(C) 25
(D) 37
(E) 44
Ans: (B)
CoT: The total of thirteen numbers = 13X9 = 117
The total of first 6 and last 6 numbers is = 6 X 5+6 X 7 = 72
So, the middle number is (117 - 72 ) = 45

Ques: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
(A) 25200
(B) 2543
(C) 2344
(D) 233445
(E) 52757
Ans: (A)
CoT: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200.

Ques: A can do a piece of work in 3 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
(A) 6hours
(B) 3hours
(C) 2hours
(D) 5hours
(E) 4hours
Ans: (B)
CoT: A's 1 hour work = 1/3;
(B + C)'s 1 hour work = 1/2;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/3 + 1/2) = 5/6
B's 1 hour work = (5/6 - 1/2) = 1/3
B alone will take 3 hours to do the work.

Ques: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 3456
(B) 4567
(C) 4789
(D) 5678
(E) 5184
Ans: (E)
CoT: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62