In a class, 14 notebooks were corrected with an ink pen and 22 notebooks were corrected with a colour pencil. If 4 notebooks were corrected with both ink pen and colour pencil, what is the total strength of the class?

Introduction / Context:
This arithmetic reasoning question involves sets and overlaps. The class has some notebooks corrected with an ink pen, some with a colour pencil, and some with both. We are told the counts for each group and asked to find the total number of students or notebooks, which represents the strength of the class. The situation is a classic example of using the principle of inclusion and exclusion to avoid double counting.

Given Data / Assumptions:

• Number of notebooks corrected with an ink pen is 14.
• Number of notebooks corrected with a colour pencil is 22.
• Number of notebooks corrected with both ink pen and colour pencil is 4.
• Each student has one notebook counted in these corrections.
• We want to find the total number of students in the class, which equals the total number of distinct notebooks.

Concept / Approach:
When two categories overlap, counting each category separately and then adding gives an overcount because items in the overlap are counted twice. The inclusion and exclusion principle tells us how to correct this. For two sets A and B, the number of distinct elements in A union B is n(A) + n(B) - n(A intersection B). Here, the ink pen group and the colour pencil group are our two sets, and the overlap is the notebooks corrected with both.

Step-by-Step Solution:
Step 1: Let A be the set of notebooks corrected with an ink pen, with n(A) = 14.Step 2: Let B be the set of notebooks corrected with a colour pencil, with n(B) = 22.Step 3: The intersection A intersection B, representing notebooks corrected with both, has n(A intersection B) = 4.Step 4: Apply the inclusion and exclusion formula for the union: n(A union B) = n(A) + n(B) - n(A intersection B).Step 5: Substitute the values: n(A union B) = 14 + 22 - 4.Step 6: Evaluate the sum: 14 + 22 = 36, then 36 - 4 = 32.Step 7: Therefore the total number of distinct notebooks, and so the strength of the class, is 32.

Verification / Alternative check:
An alternative way to think about it is to break the colour pencil group into those that are only in that group and those that overlap. There are 4 notebooks that appear in both groups. So there are 14 notebooks in the ink pen group, but 4 of those are already counted in the overlap. In the colour pencil group, 22 notebooks include those same 4. If we list the non overlapping ones, we have 14 in ink pen plus 22 minus 4 in colour pencil only, which is 14 + 18 = 32. This matches the inclusion and exclusion result.

Why Other Options Are Wrong:
If we add 14 and 22 directly without subtracting the overlap, we get 36, which would be an overcount and does not appear as an option. Option a, 30, and option c, 28, are obtained by incorrect adjustments or guesses. Option d, 25, is too low because even the larger group alone has 22 notebooks. Only 32 correctly reflects the union of both groups without double counting.

Common Pitfalls:
The most common mistake is to ignore the overlap and simply add the two given numbers. Another mistake is to subtract the overlap twice. Remember the rule for two overlapping groups: total distinct items equals sum of individual counts minus the count of the overlap once. Drawing a simple Venn diagram can help visualise the situation clearly.

Final Answer:
The total strength of the class is 32 students.