q: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
(A) 7
(B) 4
(C) 12
(D) 19
(E) 28
a: Stream of consciousness: Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a). The answer is (D).


question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
(A) 5/18
(B) 5/12
(C) 5/19
(D) 5/15
(E) 5/11
answer: 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: How should be added in order to make 2345672 this number is divisible by 9?
Options:
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
a: Stream of consciousness: Sum of the numbers 2345672 is 29 which is not multiple of 9
Add 7 which makes the sum 36 which is multiple of 9
So digit becomes 2345679 (as we know that if sum multiple of 9 then it is divisible of 9) The answer is (C).


question: In how many ways can you seat 5 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
(A) 720
(B) 1720
(C) 48
(D) 5040
(E) 10080
answer: Stream of consciousness: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 2 chairs to sit. The remaining 4 people can sit in 4! ways. Thus the # of arrangements is 2*4! = 48. The answer is (C).


q: Calculate the value of n from the below equation: n^3âˆ’10n+20=44
Options:
(A) 1
(B) 5
(C) 3
(D) 2
(E) 4
a: Stream of consciousness: Use elimination method to find the correct option. you find that of all the options when 4 is the correct value for n The answer is (E).


q: If 10 crates have 97 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 30
(B) 10
(C) 15
(D) 20
(E) 0
a:

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
Stream of consciousness: Each crate requires 3 apples and totally there are 10 crates so required apples = 10 * 3 = 30 The answer is (A).