9ab8 is a four-digit number divisible by 12. If the number formed from the two digits ab is a multiple of 7, then ab =Options16255265

The problem states that the number 9ab8 is divisible by 12 and the number ab is divisible by 7.

Step 1: Understanding divisibility rules A number is divisible by 12 if it is divisible by both 3 and 4. A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 4 if the number formed by the last two digits is divisible by 4.

Step 2: Applying divisibility rules to 9ab8 For 9ab8 to be divisible by 3, the sum of its digits (9+a+b+8) must be divisible by 3. This simplifies to a+b+17. Since a and b are digits, their sum ranges from 0 to 18. The possible values for a+b that are divisible by 3 are 2, 5, 8, 11, 14, and 17.

For 9ab8 to be divisible by 4, the number formed by the last two digits (b8) must be divisible by 4. The only way for a two-digit number ending in 8 to be divisible by 4 is if the tens digit (b) is even. So, b must be 0, 2, 4, 6, or 8.

Step 3: Applying divisibility rule to ab The problem also states that ab is divisible by 7. The only two-digit multiples of 7 that end in an even number are 14, 28, 42, 56, and 70.

Step 4: Finding the intersection of the sets The only number that satisfies all these conditions is 56. So, ab = 56.

Therefore, the answer is 56.