The value of ab + 2c can be found if: Statements: I. The values of a and c are…

Concept

In a data-sufficiency question you do NOT compute the final value; you only decide whether the given information forces a single value for the target expression. The target is ab + 2c. A statement is sufficient only when it pins the value down for whatever the (unknown) numbers a, b and c actually are; if the value could still come out differently, that statement is insufficient.

Applying it here

1. Statement I on its own gives a and c but says nothing about b. Since ab depends on b, the expression ab + 2c would change as b changes, so the value is not forced. Statement I alone is insufficient.

2. Statement II on its own gives only the sum b + c. This neither separates b from c nor gives any value of a, so ab + 2c is not forced. Statement II alone is insufficient.

3. Now use both statements: a and c come from Statement I; the sum b + c comes from Statement II, and since c is known, b = (b + c) - c is forced as well. So a, b and c are each forced.

4. With a, b and c all forced to single values, ab + 2c is forced to a single number. The two statements together are sufficient.

Cross-check

Each statement alone misses something the expression needs (Statement I never fixes b; Statement II never fixes a), so neither is sufficient by itself; together they fix all of a, b and c, so the pair is sufficient.