q: In the Biotechnology class of 2000, there were X graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is X equal to?
Options:
(A) 69.
(B) 71
(C) 73
(D) 75
(E) 76
a: Stream of consciousness: Graduates got job = 32
Graduates continued to second degree = 45
Graduates got job and continued to second degree = 13
Graduates didn't get job and didn't continue to second degree = 9
Job No Job Total
Second Degree 13 32 45
No Second Degree 19 9 28
Total 32 41 X
Therefore X = 73 The answer is (C).

question: The total number of students in Grades 1 and 2 is 30 more than the total number of students in grades 2 and 5. How much lesser is the number of students in Grade 5 as compared to Grade 1?
Options:
(A) 20
(B) 30
(C) 10
(D) 40
(E) 15
answer: Stream of consciousness: (Grade 1 + Grade 2) - (Grade 2 + Grade 5) = 30
Grade 1 - Grade 5 = 30 The answer is (B).

q: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
Options:
(A) 1/8
(B) 1/2
(C) 1/5
(D) 1/5
(E) 1/3
a: 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 answer is (C).

question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 328
(B) 150
(C) 279
(D) 277
(E) 267
answer: Stream of consciousness: 1/2 * 20(9 + 6) = 150 cm2 The answer is (B).

q: A faucet, partially on, fills a bucket with water at a rate of r buckets per minute. If the faucet is turned up it will fill the same bucket at a rate r + 2 buckets per minute, and the same bucket would fill in 2/3 minute less. What is the value of r?
Options:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
a: Stream of consciousness: Equation: 1/r = 1/(r + 2) + 2/3
Plug options into the equation:
E fits: 1/1 = 1/(1 + 2) + 2/3 The answer is (E).

q: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
(A) 6 2/3%
(B) 6 2/8%
(C) 7 2/3%
(D) 6 5/3%
(E) 4 2/3%
a:
Stream of consciousness: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3% The answer is (A).