You are asked: "What is the value of the product KL?" Additional information: Statement A: K squared equals 4, that is K^2 = 4. Statement B: L = 0. Which option correctly describes the sufficiency of these statements for determining KL?

Introduction / Context:
This is a simple data sufficiency problem about the product of two variables, K and L. Each statement gives partial information about one of the variables. We need to decide whether either statement by itself or both together are enough to determine the value of KL. The focus is on logical sufficiency, not on overcomplicating the arithmetic.

Given Data / Assumptions:

• We want the exact value of the product KL.
• Statement A: K^2 = 4, so K is a real number whose square is 4.
• Statement B: L = 0.
• There are no further restrictions given on K or L beyond these statements.

Concept / Approach:
If the value of one of the factors in a product is zero, then the entire product is zero, regardless of the value of the other factor. This is a basic property of multiplication. On the other hand, if we only know that K^2 = 4, then K could be either +2 or -2, and without knowing L we cannot determine the product. So we check each statement separately against this simple principle.

Step-by-Step Solution:
Step 1: Consider statement A alone: K^2 = 4. This equation has two real solutions, K = 2 or K = -2.Step 2: Without any information about L, KL could be 2L or -2L, and L itself is completely unknown. So the product KL is not uniquely determined from statement A alone.Step 3: Now consider statement B alone: L = 0.Step 4: If L equals zero, then for any value of K, the product KL equals K * 0 = 0.Step 5: This means that, even without knowing K, we can be absolutely certain that KL = 0 when L = 0.Step 6: Thus statement B alone is sufficient to determine KL, while statement A alone is not.Step 7: Using both statements together does not change the conclusion, because the presence of L = 0 already fixes the product at zero.

Verification / Alternative check:
Try sample values. With statement B, let K be 2, -2 or any other number; in all cases KL = 0.With statement A alone, if L happened to be 3, KL could be 6 or -6. Different possibilities for K give different products, so KL is not fixed.This confirms that the sufficiency comes entirely from knowing L = 0.

Why Other Options Are Wrong:
Option a is wrong because K^2 = 4 does not give a single specific value of K, and L is still unknown.Option c suggests that both statements are required, but we have shown that statement B alone is enough.Option d is incorrect because at least one statement, namely B, is sufficient.Option e is wrong because together the statements clearly determine KL as 0, and so does statement B alone.

Common Pitfalls:
Overlooking the basic rule that any number multiplied by zero gives zero.Assuming that if a statement gives two possible values for one variable, it must always be insufficient, even when the other factor is fixed at zero.Thinking that knowing both K and L is always necessary, when sometimes information about only one factor is enough.

Final Answer:
Because L = 0 fixes the product regardless of K, Only statement B alone is sufficient to determine KL.