Question

Quantity A: 54% of 360
Quantity B: 150

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

Hint:

For percentage problems in quantitative comparison, look for opportunities to estimate using benchmarks like 10%, 25%, or 50%. This can save valuable time compared to performing a full calculation, especially when the quantities are far apart.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The problem requires comparing a calculated percentage of a number with a fixed integer value. We need to determine if 54% of 360 is greater than, less than, or equal to 150.
Step 2: Key Approach:
There are two main ways to solve this: by estimation or by exact calculation. Estimation is often faster in quantitative comparison questions.
Step 3: Detailed Explanation (Method 1: Estimation):
We can use a known, easy-to-calculate percentage as a benchmark. 50% is a good choice.
- First, calculate 50% of 360. 50% is equivalent to $\frac{1}{2}$.
\[ 50% \text{ of } 360 = \frac{1}{2} \times 360 = 180 \] - We know that 54% is greater than 50%. Therefore, 54% of 360 must be greater than 50% of 360.
\[ 54% \text{ of } 360>180 \] - Now, compare this result with Quantity B.
- Quantity A is greater than 180.
- Quantity B is 150.
Since $180>150$, and Quantity A is even larger than 180, it is certain that Quantity A is greater than Quantity B.
Step 3: Detailed Explanation (Method 2: Exact Calculation):
To be completely sure, we can calculate the exact value of Quantity A.
- "Percent" means "per hundred," so 54% can be written as $\frac{54}{100}$ or 0.54.
\[ \text{Quantity A} = 54% \text{ of } 360 = \frac{54}{100} \times 360 \] \[ \text{Quantity A} = 0.54 \times 360 \] \[ \text{Quantity A} = \frac{54 \times 360}{100} = \frac{54 \times 36}{10} = \frac{1944}{10} = 194.4 \] - Now, compare Quantity A (194.4) with Quantity B (150).
\[ 194.4>150 \] Both methods confirm that Quantity A is greater than Quantity B.
Step 4: Final Answer:
The calculated value of Quantity A is 194.4, which is greater than Quantity B's value of 150. Therefore, the correct answer is (A).