Question

Pranay asks Shruti to choose a three-digit number. He then asks her to form two more

3-digit numbers keeping the order of digits same i.e. either clockwise or anti-clockwise. He

then asks her to add them up and then divide the resulting answer by 37. He guarantees that there will be no remainder. What was the logic behind his guarantee​

Answer 1

Answer:

let the no.s be a x100 + b x 10 + c x 1

and, 100 x b + c x 10 + a x 1

and, 100 x c + a x 10 + b x 1

so, adding them, we will get..

(100a+10b+c) + (100b+10c+a)+(100c+10a+b)

=(100+10+1)a+(100+10+1)b+(100+10+1)c

=111a+111b+111c

=111(a+b+c)

now, dividing by 37,

we get...3(a+b+c)

so, no remainder is there.