Question

What is the value of y?
(1) y is 20% greater than x.
(2) x + y = 55.

• 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:

To solve for two variables, you need two independent equations. Look at each statement to see if it provides an equation. If you have two unique equations from the two statements, you can almost always solve for the variables.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This Data Sufficiency question asks for a specific numerical value of \(y\). We need to determine if the statements provide enough information to solve for \(y\).
Step 2: Detailed Explanation:
Analyze Statement (1):
"y is 20% greater than x." We can write this as an equation:
\[ y = x + 0.20x \]
\[ y = 1.2x \]
This is one equation with two unknown variables, so we cannot find a unique value for \(y\). Statement (1) is not sufficient.
Analyze Statement (2):
"x + y = 55."
This is also one equation with two unknown variables. It is not sufficient to solve for \(y\).
Analyze Statements (1) and (2) Together:
We now have a system of two distinct linear equations with two variables:
1) \(y = 1.2x\)
2) \(x + y = 55\)
We can solve this system. Substitute the expression for \(y\) from the first equation into the second equation:
\[ x + (1.2x) = 55 \]
\[ 2.2x = 55 \]
\[ x = \frac{55}{2.2} = \frac{550}{22} = 25 \]
Now that we have the value of \(x\), we can find \(y\):
\[ y = 1.2 \times 25 = 30 \]
Since we found a unique value for \(y\), the combination of both statements is sufficient.
Step 3: Final Answer:
Neither statement is sufficient alone, but together they are sufficient. This corresponds to option (C).