Question

${21}^{643}=25A+B.$ Find the least value that B can take ?

• A. 11
• B. 1
• C. 6
• D. 16
• E. 31

Answer 1

The correct option is A 11

Solution:Option (a)

The question is asking for the remainder when ${21}^{643}$ is divided by 25. We can use the last two digits technique to get the answer, as the remainder when a number is divided by 25, depends only on the last two digits i.e. ${21}^{643}=......61(6=2\times 3)$

when 61 is divided by 25, the remainder is 11. Answer is option (a)

For numbers ending in 1, the last two digits of a power expression $a^b$ can be determined as

The last digit is always 1

The $2^{nd}$ last digit = product of tens digit of base * unit digit of the power.