Question

abc is a 3 digited number then abc + bca + cab is not divisible by …………….

 A) a + b + c 

B) 3 

C) 37 

D) 10

Answer 1

Correct option is (D) 10

abc is a 3-digit number

\(\therefore\) abc = 100a+10b+c

Now abc+bca+cab = (100a+10b+c) + (100b+10c+a) + (100c+10a+b)

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

= 111a + 111b + 111c

= 111 (a+b+c)

= 3 \(\times\) 37 (a+b+c)

\(\therefore\) 3, 37 & (a+b+c) are factors of abc+bca+cab.

Thus, abc+bca+cab is divisible by 3, 37 and a+b+c, but not divisible by 10.

Answer 2

Correct option is  D) 10