Question

What is the value of m + n?
(1) The average of m, n, and p is 12.
(2) p = 18.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In Data Sufficiency, always focus on the exact question being asked. Here, you need the value of the *sum* \(m+n\), not the individual values of \(m\) and \(n\). Often, you can solve for a sum or difference without being able to solve for the individual variables.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a Data Sufficiency problem. We need to determine if the given statements, alone or combined, provide enough information to find a unique numerical value for the expression \(m + n\). We don't need to find the individual values of \(m\) and \(n\).
Step 2: Detailed Explanation:
Analyze Statement (1):
"The average of m, n, and p is 12."
This can be written as an equation:
\[ \frac{m + n + p}{3} = 12 \]
Multiplying both sides by 3, we get:
\[ m + n + p = 36 \]
To find \(m + n\), we can rearrange the equation:
\[ m + n = 36 - p \]
Since the value of \(p\) is unknown, we cannot determine a unique value for \(m + n\). Thus, statement (1) alone is not sufficient.
Analyze Statement (2):
"p = 18."
This statement provides the value of \(p\), but it gives no information about \(m\) or \(n\). Therefore, statement (2) alone is not sufficient.
Analyze Statements (1) and (2) Together:
From statement (1), we have the equation: \(m + n = 36 - p\).
From statement (2), we know that \(p = 18\).
We can substitute the value of \(p\) from statement (2) into the equation from statement (1):
\[ m + n = 36 - 18 \]
\[ m + n = 18 \]
With both statements, we can find a unique value for \(m + n\). Therefore, both statements together are sufficient.
Step 3: Final Answer:
Neither statement alone is sufficient, but the combination of both statements is sufficient. This corresponds to option (C).