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

1.	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» 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. Correct option is D) 10

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»

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.

Correct option is D) 10