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.

Hint:

For comparison questions, estimation is often faster than exact calculation. Relating the percentage to benchmark values like 10%, 25%, or 50% can save valuable time.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question requires comparing a percentage of a number with another number. We can either calculate the exact value or use estimation. 

Step 2: Key Formula or Approach: 
To find the percentage of a number, we can use the formula: 
\[ \text{Percentage Value} = \frac{\text{Percentage}}{100} \times \text{Total Value} \] Alternatively, we can use estimation. Notice that 54% is slightly more than 50% (which is half). 

Step 3: Detailed Explanation: 
Method 1: Estimation 
We know that 50% of 360 is half of 360. 
\[ 50% \text{ of } 360 = \frac{1}{2} \times 360 = 180 \] Since 54% is greater than 50%, the value of Quantity A must be greater than 180. 
Quantity B is 150. 
Since Quantity A $>$ 180 and Quantity B = 150, it is clear that Quantity A is greater. 
Method 2: Exact Calculation 
\[ \text{Quantity A} = 54% \text{ of } 360 = \frac{54}{100} \times 360 \] \[ = 0.54 \times 360 \] \[ = 194.4 \] 

Step 4: Final Answer: 
Comparing the two quantities: 
\[ 194.4>150 \] Therefore, Quantity A is greater than Quantity B.