Question

What is the sum of the real numbers a, b, c? I) $a+c=4$ II) a, b, c are in arithmetic progression

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

For 3 terms in AP, the sum is always 3 times the middle term.

Answer 1

The Correct Option is C

Step 1: Concept
In an Arithmetic Progression (AP) of three terms $a, b, c$, the middle term $b$ is the average of the first and last terms: $b = \frac{a+c}{2}$.

Step 2: Meaning
We want to find $S = a+b+c$.

Step 3: Analysis
Statement I only gives $a+c=4$. Statement II tells us $b = (a+c)/2$. Combining them, we find $b = 4/2 = 2$. Then $S = (a+c) + b = 4 + 2 = 6$.

Step 4: Conclusion
Neither statement alone can find the sum, but together they do. Final Answer: (C)