Question

f the three-digit number 4 3 x is divisible by 9, what is the value of x ?a) 1
(b) 2
(c) 3
(d) 4.​

Answer 1

Answer:

2 is the correct answer

Step-by-step explanation:

“43x” should be divisible by 3, for that it should be divisible by 3*3 or 3

Divisibility of 3 is sum of digits is divisible by 3

So 4 + 3 + x should be divisible by 3 and 0 <= x <= 9

The only solution for this is 2

So the number is 432 which is also divisible by 3

Hence x=2

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Answer 2

To be able to understand the solution for this question, we need to know about the divisibility of the number 9.

DIVISIBILITY OF THE NUMBER 9:

It states that “a number divisible by 9 should have the sum of its digits equal to a multiple of 9”.

For example: Sum of the digits of the number 585 is 5+8+5=185+8+5=18 and 18 is a multiple of 9. Therefore, 585 will be divisible by 9. We can check this statement to be true because 9×65=5859×65=585 .

Now, here in this question we know that 24x is divisible by 9. So, the relation between the digits and multiple of 9 will be:

Let mm be a factor of the multiple of 9.

22

divisibility criteria of a number that is divided by 9:-

sum of digits of that number should be divisible by 9.

here number is represented as 24x

so the sum will be 2+4+x i.e 6+x

6+x may be 9,18,27…

since x is a single digit.

so 6+x=9

x=9–6=3

hence the value of x will be 3.