Question

What is the value of \(w + q\)?
(1) \(3w = 3 - 3q\)
(2) \(5w + 5q = 5\)

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient to answer the question asked.
• E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Hint:

In Data Sufficiency, be alert for questions that ask for the value of an expression (like \(x+y\)) rather than individual variables. Often, a single equation can be rearranged to solve for the expression directly, even if it's impossible to solve for the individual variables.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks for the value of a specific expression, \(w + q\), not the individual values of \(w\) and \(q\). We need to determine if the given statements can be manipulated to find the value of \(w+q\).
Step 2: Detailed Explanation:
Analyze Statement (1): \(3w = 3 - 3q\).
Our goal is to find the value of \(w+q\). Let's rearrange the equation to group the \(w\) and \(q\) terms together. Add \(3q\) to both sides of the equation: \[ 3w + 3q = 3 \] Now, we can factor out the common term, 3, from the left side: \[ 3(w + q) = 3 \] Divide both sides by 3: \[ w + q = 1 \] This statement provides a unique value for the expression \(w + q\). Therefore, statement (1) is sufficient.
Analyze Statement (2): \(5w + 5q = 5\).
Again, our goal is to find the value of \(w+q\). We can factor out the common term, 5, from the left side of the equation: \[ 5(w + q) = 5 \] Divide both sides by 5: \[ w + q = 1 \] This statement also provides a unique value for the expression \(w + q\). Therefore, statement (2) is sufficient.
Step 3: Final Answer:
Each statement, by itself, is sufficient to determine the value of \(w+q\).