question: If 20m n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m 1
(B) 4m
(C) 6m
(D) 7m
(E) 6m/5
answer: Stream of consciousness: 20m - n = p
Add n to both sides:
20m = n + p
Add m to both sides:
21m = n + p + m
Now, divide both sides by 3
7m = (n + p + m)/3 = the average of n, p, and m The answer is (D).

q: How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?
Options:
(A) 3
(B) 4
(C) 8
(D) 10
(E) 12
a: Stream of consciousness: The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111. The answer is (A).

question: There are a total of 15 numbers with an average of 11. The average of first seven numbers is 14 and the average of last seven numbers is 6. What is the middle number?
Options:
(A) 31
(B) 24
(C) 29
(D) 25
(E) 21
answer: Stream of consciousness: The total of 15 numbers = 15X11 = 165
The total of first 7 and last 7 numbers is = 7 X 14+7 X 6 = 140
So, the middle number is (165 - 140 ) = 25 The answer is (D).

q: In how many different ways can the letters of the word "AIM" be rearrangement?
Options:
(A) 4
(B) 2
(C) 7
(D) 9
(E) 6
a: Stream of consciousness: Option 'E'
The total number of arrangements is
3P3 = 3! = 6 The answer is (E).

question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 21
(B) 20
(C) 17
(D) 12
(E) 18
answer: Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 70 = 20 The answer is (B).

question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 2 days?
Options:
(A) 2/5
(B) 1/6
(C) 1/4
(D) 1/9
(E) 2/6
answer:
Stream of consciousness: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 2 days = 2 (1/18) = 1/9. The answer is (D).