Question

Question 10

In the given question, out of four options, only one is correct. Write the correct answer.

A six- digit number is formed by repeating a three-digit number. For example, 256256, 678678 etc. Any number of this form is divisible by
(a) 7 only
(b) 11 only
(c) 13 only
(d) 1001

Answer 1

Let the six-digit number be abcabc, the
= 100000 $\times$ a + 10000b + 1000c + 100a +10b + c
= a(100000 + 100) + b(10000 + 10) + c(1000 + 1)
= a(100100) + b(10010) + c(1001) = 1001(a $\times$ 100 + b $\times$ 10 + c)
Hence, it is divisible by 1001.