Question

If a + n = b, what is the value of n?
(1) b = 5
(2) b + 5 = a

• 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 algebraic data sufficiency, always start by simplifying the question. Here, "what is the value of n?" is the same as "what is the value of b-a?". Then, check if each statement provides the value of that specific expression, not necessarily the individual variables.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the value of the variable \(n\). We are given an equation relating \(a\), \(n\), and \(b\). To find \(n\), we need to isolate it.
From the given equation, \(a + n = b\), we can write \(n = b - a\).
So, the question is effectively asking for the value of the expression \(b - a\).
Step 2: Detailed Explanation:
Analyzing Statement (1):
This statement gives us \(b = 5\).
Substituting this into our rearranged equation for \(n\):
\[ n = 5 - a \]
Since the value of \(a\) is unknown, we cannot determine a unique value for \(n\). Therefore, statement (1) alone is not sufficient.
Analyzing Statement (2):
This statement gives us the equation \(b + 5 = a\).
We can rearrange this equation to find the value of \(b - a\).
\[ b - a = -5 \]
Since we know that \(n = b - a\), we can directly substitute this value:
\[ n = -5 \]
This gives a unique value for \(n\). Therefore, statement (2) alone is sufficient.
Step 3: Final Answer:
Statement (2) alone is sufficient to find the value of \(n\), while statement (1) alone is not. Therefore, the correct option is (B).