q: Find the third proportional to 2 and 10?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 50
a: Stream of consciousness: Formula = Third proportional = (b b)/a
A = 2 and B = 10
(10 10)/ 2 = 100/2 = 50 The answer is (E).

question: 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
answer: Stream of consciousness: Option 'E'
The total number of arrangements is
3P3 = 3! = 6 The answer is (E).

q: Find the largest 4 digit number which isexactly divisible by 88?
Options:
(A) 4567
(B) 3588
(C) 9944
(D) 5465
(E) 6784
a: Stream of consciousness: Largest 4 digit number is 9999
After doing 9999 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 The answer is (C).

question: In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 9^5 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
answer: Stream of consciousness: 9 people can be prized with 5 distinct prizes in 9^5 ways The answer is (A).

q: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
(A) 5/16
(B) 5/12
(C) 5/87
(D) 5/56
(E) 5/38
a: Stream of consciousness: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12 The answer is (B).

q: Which of the following is not divisible by 3?
Options:
(A) 10394
(B) 15363
(C) 29340
(D) 30753
(E) 41715
a:
Stream of consciousness: Divisibility rule of 3: The sum of the digits of the number should be divisible by 3
Option A: 10394, Sum = 17. Not divisible by 3. Hence the number 10394 is also not divisible by 3
Option B: 15363, Sum = 18, Divisible by 3
Option C: 29340, Sum = 18, Divisible by 3
Option D: 30753, Sum = 18, Divisible by 3
Option E: 41715, Sum = 18, Divisible by 3 The answer is (E).