Eighty five is what percentage of 352, expressed to two decimal places?

Introduction / Context:
This question is a basic percentage calculation where a smaller number is compared to a larger one, and we are asked what percentage the smaller number represents of the larger number. Such direct fraction to percentage conversions are very common in aptitude and data interpretation sections, and fluency with them helps in tackling more complex ratio and percentage problems later.

Given Data / Assumptions:

• Smaller number is 85.
• Larger number is 352.
• We must find what percentage 85 is of 352.
• The answer should be accurate to two decimal places, as seen in the options.

Concept / Approach:
To find what percentage one number is of another, we use the formula: Percentage = (part / whole) * 100. Here, 85 is the part and 352 is the whole. After forming the fraction 85 / 352, we convert it to a decimal and multiply by 100 to get the percentage. Finally, we compare this with the options to select the closest matching value.

Step-by-Step Solution:
We need to compute (85 / 352) * 100.First, calculate the fraction 85 / 352.This division gives approximately 0.241477 when rounded to six decimal places.Multiply this by 100 to convert to a percentage: 0.241477 * 100 = 24.1477.Rounded to two decimal places, this is 24.14%.Therefore, 85 is approximately 24.14% of 352.

Verification / Alternative check:
For a quick check, estimate using nearby proportions. Half of 352 is 176, so 85 is slightly less than half of 176, and half of 352 is 50%. Since 85 is much less than 176 and a little less than 88 (which would be exactly one quarter of 352), it is reasonable that the percentage is slightly less than 25%. Among the options, 24.14% is the only value just under 25%, while the others are either far below or above in comparison. This rough reasoning supports the calculated answer.

Why Other Options Are Wrong:
21.5% and 23.68% are both lower than 24.14% and do not match the exact division result.

25.47% is higher than the true value and would correspond to a larger part than 85 for the same whole of 352.

Common Pitfalls:
Sometimes students inadvertently compute 352 as a percentage of 85 instead of 85 as a percentage of 352, leading to the reciprocal fraction. Another mistake is to round off too early in the calculation, which can slightly shift the percentage. It is better to keep sufficient decimal places during intermediate calculations and only round to two decimal places at the end, especially when answer options are close to each other.

Final Answer:
Eighty five is approximately 24.14% of 352.