Question

A number of the form xxyy when divided by 11 gives a number which is again divisible by 11. If x-y=1 , find the number.

Answer 1

Heya user,

we can write the no. as xxyy = 1100x + 11y
Dividing it by 11, we get 100x + y where 0 < (x,y) < 10

Hence, applying divisibility rule for 11,
x + y = 11 is the only possible eqn. that would satisfy our needs..

Also, x - y = 1
Hence, 2x = 11 + 1 or x = 6 and y = 5;

.'. The only such no. is  11[100*6 + 5 ] = 6655

VERIFICATION ---> [ 6655/11 = 605 ]; [ 11 | 605 ]; [ 6 - 5 =1 ]

Hence our no. is 6655