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Choose whether the given statement is true or false.

The last two digits of 17256 are 18.

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True

False

answer is B.

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Detailed Solution

For finding last two digits we have to find the remainder of 17256
So, we apply binomial expansion.

= (10 + 7) 256 = 256 C 0 100 7 256 − 0 + 256 C 1 101 7 256 − 1

Higher terms which contain 102 which are divisible by 100.

= 256 C 0 100 7 256 − 0 + 256 C 1 101 7 256 − 1

We get last digit by last digit of

256 C 0 100 7 256 − 0

the last digit of 7256 is 1.
Second last digit is the second last digit of

256 C 1 101 7 256 − 1

= 256 × 7255 × 10

= 6 × 3
Second last digit = 8 only the last digit (Because last digit of 7255 = 3)
So, the second last and last are 81.
Hence, the given statement is false.
The correct statement is: “The last two digits of 17256 are 81.”

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