question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 5 strokes ?
Options:
(A) 31/32
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
answer: Stream of consciousness: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
So removed = 1- 1/32 = 31/32 The answer is (A).

q: 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) 49 Years
(B) 51 Years
(C) 53 Years
(D) 54 Years
(E) 55 Years
a: 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 (A).

question: 30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 16
answer: Stream of consciousness: Since average price of a pencil = 2
Price of 75 pencils = 150
Price of 30 pens = (630 150) = 480
Average price of a pen = 48060 = 16 The answer is (E).

q: How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 55
(C) 33
(D) 22
(E) 11
a: Stream of consciousness: (60/100) * 50 (40/100) * 30
30 - 12 = 18 The answer is (A).

question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 2 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other one children on either side of him, how many seating arrangements are possible?
Options:
(A) 3
(B) 4
(C) 6
(D) 8
(E) 10
answer: Stream of consciousness: Mother has a fixed place and father, so there are 3*2 ways to arrange the children, hence The answer is (C).

question: If 10 crates have 99 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 0
answer:
Stream of consciousness: Each crate requires 1 apples and totally there are 10 crates so required apples = 10 * 1 = 10 The answer is (B).