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Question

The last two digits of the number 3400 are


A

81

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B

43

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C

29

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D

01

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Solution

The correct option is D

01


We want to find the last two digits of 3400. If we can expand in terms of some number which is a multiple of 10 or 100, we can easily find the last two digits. We know 34 = 81.

(3)400=81100

(3)400=(80+1)100

(80+1)100=100C0(80)100+100C1(80)499+100C2(80)498+..........+100C99(80)1+100C100

(80+1)100=100C0(80)100+100C1(80)499+100C2(80)498+..........+100×(80)1+1

The terms other than the last two terms have more than two hundreds.So the only terms which will decide the last two digits are the last two terms.

(80+1)100=100C0(80)100+100C1(80)499+100C2(80)498+...........+8000+1

The last two digits are 0 and 1


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