Question

Question 5

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

The sum of all the numbers formed by the digits x, y and z of the number xyz is divisible by
(a) 11
(b) 33
(c) 37
(d) 74

Answer 1

We have, xyz + yzx + zxy
= (100x + 10y + z) + (100y + 10z + x) + (100z + 10x + y) ...........(i)
= 100x + 10x + x + 10y + 100y + y + z + 100z + 10z
= 111x + 111y + 111z = 111(x + y + z)
= $3\times 37\times (x+y+z)$
Hence, Eq. (i) is divisible by 37, but not divisible by 11, 33 and 74.