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An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?

An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number? Correct Answer 8

Option (1) is correct.

The identity Card number ABCDEFG is 7 digit number.

Step 1: The number is divisible by 9, which means the sum of digits is divisible by 9.

1 + 2 + 4 + 5 + 7 + 8 + 9 = 36.

Step 2: After deleting the first digit from the right, the resulting number is divisible by 6.

The number is divisible by 6, which means the number that is divisible by 3 and 2 both. If we delete any single-digit number from a number divisible by 9, the number is only divisible by 3 if the deleting digit is also divisible by 3, so that sum is divisible by 3.

Out of (1, 2, 4, 5, 7, 8, 9) only 9 is divisible by 3, So, the first digit from the right is 9 and the second digit from the right must be even as it is also divisible by 2.

Step 3:  After deleting two digits from the right of the original number, the resulting number is divisible by 5.

The number is divisible by 5, which means the last digit is 0 or 5. So, the third digit from the right must be 5. 

Step 4: After deleting three digits from the right of the original number, the resulting number is divisible by 4.

The number is divisible by 4, which means the last two digits are divisible by 4.

Step 5: After deleting four digits from the right of the original number, the resulting number is divisible by 3.

The number is divisible by 3, which means the sum of digits is divisible by 3. So the sum of the first three digits of the number from the right is divisible by 3.

Step 6: After deleting five digits from the right of the original number, the resulting number is divisible by 2 which means the second digit is even.

Possible outcomes are 7412589  and 1472589. Possible values for the sum of the middle 3 digits of the number are 8 (7412589) and 14 (1472589).

Hence, the correct answer is an option(1) i.e., 8.

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