Verified answer

The digit ∆ must be equal to 6 for the number 20101∆17 to be divisible by 9.

Given:

An 8-digit number 20101∆17 is divisible by 9.

To find:

What digit does ∆ stand for?​

Solution:

To determine the value of the digit (∆) that makes the 8-digit number 20101∆17 divisible by 9, we can use the divisibility rule for 9.

According to the rule, a number is divisible by 9 if the sum of its digits is divisible by 9.

Let's calculate the sum of the digits in the number:

=> 2 + 0 + 1 + 0 + 1 + ∆ + 1 + 7 = 12 + ∆

Here (12 + ∆) should leave a remainder of 0 when divided by 9.

To find the value of ∆, we need to check which digit satisfies this condition.

For ∆ = 6: (12 + 6) = 18 (divisible by 9)

Therefore,

The digit ∆ must be equal to 6 for the number 20101∆17 to be divisible by 9.

#SPJ1

Explanation:

To determine the value of the digit represented by ∆ in the 8-digit number 20101∆17, we can use the divisibility rule for 9. According to the rule, a number is divisible by 9 if the sum of its digits is divisible by 9.

Let's calculate the sum of the known digits in the number:

2 + 0 + 1 + 0 + 1 + 1 + 7 = 12

For the number to be divisible by 9, the sum of its digits must also be divisible by 9. Since 12 is not divisible by 9, we need to find the digit that makes the sum divisible by 9.

The sum of the known digits (12) plus the value of ∆ must be divisible by 9. Therefore, we need to find a number between 0 and 9 that, when added to 12, results in a sum divisible by 9.

Let's check the numbers from 0 to 9:

12 + 0 = 12 (not divisible by 9)

12 + 1 = 13 (not divisible by 9)

12 + 2 = 14 (not divisible by 9)

12 + 3 = 15 (not divisible by 9)

12 + 4 = 16 (not divisible by 9)

12 + 5 = 17 (not divisible by 9)

12 + 6 = 18 (divisible by 9)

Therefore, the digit represented by ∆ in the number 20101∆17 is 6.

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