Question

If ( p ) is a positive odd integer, what is the remainder when ( p ) is divided by 4?

(a) 0

(b) 1

(c) 2

(d) 3

Answer 1

When a positive odd integer is divided by 4, the possible remainders are 1, 2, and 3.

Step-by-step explanation:

When a positive odd integer is divided by 4, the possible remainders are 1, 2, and 3. This is because if you divide any odd integer by 4, the quotient will be an even integer and the remainder will be 1, 2, or 3. Therefore, the correct answer is (b) 1.

Option (a) is incorrect as 0 is the remainder when a number is divisible by 4, which is not the case for odd numbers. Option (c) is also incorrect because 2 would be the remainder if p were an even number, but p is given as odd. Thus, the correct answers are options (b) and (d), which are 1 and 3, the possible remainders when dividing an odd number by 4.