Question

x is positive number and y is 30 percent of x
Column A: 25. percent of y
Column B: 55 percent fo x

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When a problem involves a "percent of a percent," it's often easiest to convert all percentages to decimals and multiply. This avoids confusion and simplifies the comparison.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem requires comparing two quantities that are expressed as percentages of different variables, where the variables themselves are related.
Step 2: Key Formula or Approach:
First, translate the given relationship between \(y\) and \(x\) into a mathematical equation. Then, substitute this relationship into the expression in Column A to express both columns in terms of the same variable, \(x\).
Step 3: Detailed Explanation:
We are given that "\(y\) is 30 percent of \(x\)". This can be written as:
\[ y = 0.30 \times x \] Now let's evaluate Column A in terms of \(x\).
Column A: 25 percent of \(y\).
\[ 0.25 \times y = 0.25 \times (0.30x) = 0.075x \] So, the quantity in Column A is equivalent to 7.5% of \(x\).
Column B: 55 percent of \(x\).
This is simply \(0.55x\).
Comparison:
We are comparing \(0.075x\) (Column A) with \(0.55x\) (Column B).
Since we are given that \(x\) is a positive number, we can compare the decimal coefficients.
\[ 0.075<0.55 \] Therefore, the quantity in Column B is greater than the quantity in Column A.
Step 4: Final Answer:
By expressing Column A in terms of x, we find it is \(0.075x\), which is smaller than Column B's \(0.55x\).