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Question

Find the last two digits of 31997.

A
67
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B
63
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C
80
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D
56
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Solution

The correct option is B 63
This is same as asking what is remainder when 31997÷100
3481mod100
3861mod100
31241mod100
31621mod100
3201mod100

Now, 340,360,380,3100,....,31980 all are 1mod100

We know 31621mod100

31721×3mod100

31763mod100

3199731980×317

since, 319801mod100

and 31763mod100

3199763mod100

Last two digit is 63

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