10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/1
(E) 1/2
Answer and stream of consciousness: (C)
Stream of consciousness: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5


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
(B) 88
(C) 25
(D) 18
(E) 11
Answer and stream of consciousness: (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


What is the are of an equilateral triangle of side 16 cm?
Options:
(A) 66√3 cm2
(B) 74√3 cm2
(C) 64√3 cm2
(D) 64√5 cm2
(E) 14√3 cm2
Answer and stream of consciousness: (D)
Stream of consciousness: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;


The speed of a car is 90 km in the first hour and 42 km in the second hour. What is the average speed of the car?
Options:
(A) 89 kmph
(B) 92 kmph
(C) 75 kmph
(D) 65 kmph
(E) 66 kmph
Answer and stream of consciousness:

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
(E)
Stream of consciousness: S = (90 + 42)/2 = 66 kmph