JEE Mathematics 2023 Question with Solution

Given: $S_K = \frac{1 + 2 + \dots + K}{K}$.

Find: Which statement about $A, B, C, D$ is correct.

From the solution,

and hence

The extracted solution then states that on simplifying the summation and comparing the required terms, we obtain

Now check the options using these values:

and

Therefore,

So the correct statement is $A + B$ is divisible by $D$. Therefore, the correct option is A.

Given: the solution provides the final values $A = 24, B = 2, C = 9, D = 13$.

Find: Which option matches these values.

Evaluate each relevant expression:

Now test the divisibility claims:

• $26$ is divisible by $13$.
• $26$ is not divisible by $5$.
• $46$ is divisible by $2$, so the statement "not divisible by $B$" is false.
• $39$ is not divisible by $5$.

Hence only the first statement is true. Therefore, the correct option is A.