Question

A number when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder is:

A. 15
B. 18
C. 12
D. 9

Answer 1

The remainder when the number is divided by 19 is 21.

Step-by-step explanation:

To find the remainder when a number is divided by 19, we can use the concept of congruence. Since the original number leaves a remainder of 21 when divided by 114, we can express it as:

x ≡ 21 (mod 114)

Now, we can simplify this congruence by finding a number that is equivalent to 21 mod 114 and also congruent to 21 mod 19. The number 57 satisfies these conditions:

57 ≡ 21 (mod 114)

57 ≡ 21 (mod 19)

Therefore, the remainder when the original number is divided by 19 is 21.