There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest test score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.

Consider the following statements:

1. The average score of Class-B will definitely decrease.

2. The average score of Class-A will definitely increase.

Which of the above statements is/are correct?

The correct option is 1 only.

Let us analyze the given information step-by-step:

1. Class-A has 25 students. The highest score in Class-A is 21 and the lowest score is 17. Therefore, every student in Class-A has a score between 17 and 21 (inclusive).

2. Class-B has 30 students. The highest score in Class-B is 30 and the lowest score is 22. Therefore, every student in Class-B has a score of at least 22.

3. This means that the average score of Class-B prior to shifting is strictly greater than 22, because all students in Class-B scored between 22 and 30.

Now, let us examine the two statements after moving 4 students from Class-A to Class-B:

Analysis of Statement 1:

The 4 students shifted from Class-A have scores of at most 21 (since the maximum possible score in Class-A is 21).

Since the existing average score of Class-B is strictly greater than 22, adding any 4 students with scores of at most 21 (which are strictly lower than the current Class-B average) will pull the average down.

Therefore, the average score of Class-B will definitely decrease. Hence, Statement 1 is correct.

Analysis of Statement 2:

The average of Class-A depends on which 4 students are transferred.

If the 4 students who leave Class-A have scores lower than the initial average of Class-A, then Class-A's average will increase.

However, if the 4 students who leave have scores higher than or equal to the initial average of Class-A (for example, if all 4 students had the highest score of 21), the average score of Class-A will decrease or stay the same.

Since we do not know the exact individual scores of the 4 transferred students relative to Class-A's average, we cannot state that Class-A's average will definitely increase.

Therefore, Statement 2 is not necessarily correct.

Thus, only Statement 1 is definitely correct.