question: From among the 35 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1190
(E) 1460
answer: Stream of consciousness: There are 35 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 35 ways. When one person is appointed as leader, we are left with 35 students. Out of these 34 teachers, we can select one class representative. So, a class representative can be selected in 34 ways. Hence, the number of ways in which a leader and class representative can be selected = 35 x 34 = 1190 The answer is (D).

q: In how many different ways can the letters of the word "POLICE" be rearrangement?
Options:
(A) 710
(B) 725
(C) 720
(D) 770
(E) 722
a: Stream of consciousness: Option 'C'
The total number of arrangements is
6P6 = 6! = 720 The answer is (C).

question: There are five same model cars parked in the same direction in parking. If 3 cars are red, 1 is black and 1 is green, in how many ways they can be arranged in the parking?
Options:
(A) 10 ways.
(B) 20 ways.
(C) 30 ways.
(D) 40 ways.
(E) 50 ways.
answer: Stream of consciousness: 5!/(3!*1!*1!) = (5*4*3*2*1)/(3*2*1) = 120/6 = 20 ways. The answer is (B).

q: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is?
Options:
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220060
a: Stream of consciousness: (555 + 445) * 2 * 110 + 60 = 220000 + 60 = 220060 The answer is (E).

question: A man rows his boat 90 km downstream and 5' km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
(A) 7 kmph
(B) 5 kmph
(C) 2 kmph
(D) 8 kmph
(E) 1 kmph
answer: Stream of consciousness: Speed downstream = d/t = 90/(3) = 30 kmph
Speed upstream = d/t = 51/(3) = 17 kmph
The speed of the stream = (30 - 17)/2 = 7 kmph The answer is (A).

question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?
Look at this series: 88, 3, 80, 12, __, 21 ... What number is missing?
Options:
(A) 72
(B) 78
(C) 68
(D) 30
(E) 70
answer:
Stream of consciousness: A
72
This is an alternating addition and subtraction series. In the first pattern, 8 is subtracted from each number to arrive at the next. In the second, 9 is added to each number to arrive at the next. The answer is (A).