Question

When N DIVIDED 5 leaves a remainder 2 , find the one's digit of N

Answer 1

Answer:

Unit digit of N is either 2 or 7.

Step-by-step explanation:

If N leaves 2 as remender when divided by 5,

N = 5q + 2 ...............(1)

Unit place of a number is the remainder when it is divided by 10. So we will find out the remainder of N when divided by 10.

Case 1 q = 2m(even)

N ≡ 5q + 2 ( mod 10)

(This means that N and 5q + 2 leaves same remainder when divided by 10)

or N ≡ 5*2m + 2 ( mod 10)

or N ≡ 10m + 2 ( mod 10)

or N ≡ 2 ( mod 10)

Hence 2 is the unit digit in this case.

Case 2 q = 2m + 1(odd)

N ≡ 5q + 2 ( mod 10)

or N ≡ 5(2m + 1) + 2 ( mod 10)

or N ≡ 10m + 5 + 2 ( mod 10)

or N ≡ 10m + 7 ( mod 10)

or N ≡ 7 (mod 10)

Hence, 7 is the unit digit in this case.