Question

What is the missing digit in the number 432 _ _ _ _ _ _ 687 if the number is divisible by 9?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

For divisibility by 9, digit sum must be a multiple of 9.

Answer 1

The Correct Option is B

To determine the missing digits in the number \(432\_ \_ \_ \_ \_ \_ 687\), we must ensure it is divisible by 9. A number is divisible by 9 if the sum of its digits is also divisible by 9.

Let the missing digits be represented by \(a, b, c, d, e, f\). Thus, the complete number is represented as \(432abcdef687\).

Taking the sum of the known digits:

• Sum of the digits \(4 + 3 + 2 + 6 + 8 + 7 = 30\)

Therefore, the equation for the sum of all digits becomes:

\(30 + a + b + c + d + e + f\)

This sum must be divisible by 9.

Initially, let's test the possible given options to insert one digit to make up multiple missing digits:

• If we assume \(abcdefgh = 600000\), we wish \(30 + 6 = 36\) is divisible by 9. Since 36 is divisible by 9, the missing digit represented must include a "6" to satisfy the problem;

Thus, the missing digits include "6". Testing other placeholders (which makes the year variate vast steps without obstacles), we consider:

• If any combination from possibilities there could be ruled based on decimals ignored.

Thus, the most immediate and smallest rest which would still remain for resolution and complete arrangement fulfilling numbers into calculations below, being that the correct viable missing representation turns as numerical "6".

Therefore, the correct answer is indeed 6.