In a race with 30 runners where 8 trophies will be given to the top 8 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 8^8 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways

8 people can be prized with 8 distinct prizes in 8^8 ways So the answer is: (A).

In Badminton game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4

In Badminton game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. So the answer is: (C).

If x is an even integer, which of the following is an even integer?
Options:
(A) 3x-3
(B) x+x^2
(C) 5x-3
(D) 2x+1
(E) 9x-5

Plug in an even integer; in this case 2
(3*2)-3 = 6-3 = 3 Odd
2+2^2 = 6 Even
(5*2)-3 = 10 - 3 = 7 Odd
(2*2)+1 = 4 + 1 = 5 Odd
(9*2)-5 = 18 - 5 = 13 Odd So the answer is: (B).

Sukhbir is taller than Randhir but not as tall as Ajit. If Manoj is taller than Nitin, who is shorter than Ajit, then who among them is the shortest?
Options:
(A) Nitin
(B) Sukhbir
(C) Manoj
(D) Data inadequate
(E) None of these
Data Inadequate. As No relation is given among Randhir and Nitin. So the answer is: (D).