Reasoning: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34
Ans: (A)
Question: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
Options:
(A) 34
(B) 677
(C) 197
(D) 177
(E) 191

Reasoning: (x - 1)! = (x - 2)! * (x-1)
(x - 1)!/(x-2)! = x - 1
Ans: (E)
Question: Which of the following is equal to (x-1)!/(x-2)!?
Options:
(A) x-1
(B) 1+(1/x)
(C) 1
(D) x+1
(E) x-1

Reasoning: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
Ans: (A)
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
(A) 63
(B) 25
(C) 40
(D) 65
(E) 98

Reasoning: Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Ans: (C)
Question: If a and b are unique prime integers, which of the following must be even?
Options:
(A) ab
(B) a2b
(C) 2a2b
(D) 2ab
(E) ab^2