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 must be divisible by 3. 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.

Step 3: Applying divisibility rule to ab The problem also states that ab is divisible by 7.

Step 4: Checking the options Now we check the options given for ab (16, 25, 52, 65) to see which ones meet all these conditions.

Option 1: 16 16 is divisible by 7? No. So, 16 is not the answer.

Option 2: 25 25 is divisible by 7? No. So, 25 is not the answer.

Option 3: 52 52 is divisible by 7? Yes. Is the sum of the digits (5+2=7) divisible by 3? Yes. Is the tens digit (5) even? No. So, 52 is not the answer.

Option 4: 65 65 is divisible by 7? No. So, 65 is not the answer.

Therefore, none of the options given make 9ab8 divisible by 12 and ab divisible by 7. There seems to be a mistake in the problem or the options provided.