question: 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
answer: 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).


q: There are 15 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/3. How many blue balls were there in the beginning?
Options:
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
a: Stream of consciousness: 7 = 3 blue balls + 12 / 3 The answer is (D).


question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
(A) 29 Years
(B) 32 Years
(C) 37 Years
(D) 49 Years
(E) 50 Years
answer: Stream of consciousness: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years The answer is (D).


q: On 8th Feb, 1995 it was Wednesday. The day of the week on 8th Feb, 1994 was
Options:
(A) wednesday
(B) Tuesday
(C) Thursday
(D) Friday
(E) None
a: Stream of consciousness: 1994 being an ordinary year, it has 1 odd day. So, the day on 8th Feb, 1995 is one day beyond the day on 8th Feb, 1994. But, 8th Feb, 1995 was Wednesday. 8th Feb, 1994 was Tuesday. The answer is (B).


question: If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?
Options:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
answer: Stream of consciousness: Tried to locate a '0' ending multiple of 8 between 500599
Only 560 is present
560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5 The answer is (A).


question: Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year’s original revenues did company Z have left after its marketing and maintenance expenditures?
Options:
(A) 5/14
(B) 1/2
(C) 17/28
(D) 9/14
(E) 9/11
answer:

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: Total revenues = x
Spent on marketing = x/4
Remaining amount = x-x/4 = 3x/4
1/7 of the remainder on maintenance of its facilities = 3x/4*1/7 = 3x/28
Amount left = 3x/4-3x/28 = 9x/14 The answer is (D).