A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

Question:
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

[A].

1, 2

[B].

2, 3

[C].

3, 2

[D].

4, 1

Answer: Option B

Explanation:

4 | x y = (5 x 1 + 4) = 9
——–
5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37
——–
| 1 -4

Now, 37 when divided successively by 5 and 4, we get

5 | 37
———
4 | 7 – 2
———
| 1 – 3

Respective remainders are 2 and 3.