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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


Options:
A .  1,2
B .  2,3
C .  3,2
D .  4,1
Answer: Option B

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.



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