In a class, each student scored a different rank. Aman's rank is 11th from the top and Nikhil's rank is 13th from the bottom. Only three students ranked between Aman and Nikhil. If the total number of students is an odd number divisible by 3, how many students are there in total in the class?

Solution

Let's solve this step by step: 1. Aman's rank is 11th from the top. 2. Nikhil's rank is 13th from the bottom. 3. Only three students ranked between Aman and Nikhil. First, let's find the total number of students from the information about Aman and Nikhil: Aman's position from the top + Nikhil's position from the bottom - 1 (since Aman and Nikhil are counted twice in the total) = Total number of students 11 + 13 - 1 = 23 Now, since there are three students ranked between Aman and Nikhil, we add 3 to 23: 23 + 3 = 26 So, the total number of students is 26. However, we need to check if this number is divisible by 3 and odd. 26 is even, so let's try the next odd number: 27 27 is divisible by 3 and is odd. So, the correct answer is option 4. 27.