Without calculating every step in full detail, estimate the value of 24.97% of 84.01 divided by 6.995 and choose the closest integer value from the options.

Introduction / Context:
This problem examines your ability to estimate numerical expressions involving percentages, division, and decimals. Estimation skills are very useful in competitive exams where exact arithmetic for every question is time consuming, so being able to approximate quickly is an important aptitude skill.

Given Data / Assumptions:

• The expression is 24.97% of 84.01 divided by 6.995.
• We are asked to choose the closest integer, not an exact decimal result.
• Percentages must be converted to decimal form before multiplication.

Concept / Approach:
First, interpret 24.97% as approximately 25%, and 84.01 as approximately 84. This makes mental calculation easier while staying close to the true value. Then compute 25% of 84, which equals a quarter of 84. Finally, divide this approximate result by about 7, since 6.995 is very close to 7. The final estimate should guide us to the nearest integer among the options.

Step-by-Step Solution:
Approximate 24.97% as 25%, so the decimal is 0.25.Approximate 84.01 as 84 for easier computation.Compute 25% of 84: 0.25 * 84 = 21.Approximate the denominator 6.995 as 7.Compute the estimated value: 21 ÷ 7 = 3.

Verification / Alternative check:
We can also compute more accurately. 24.97% of 84.01 is 0.2497 * 84.01, which is slightly less than 21 but very close. Dividing that by 6.995, which is very close to 7, will result in a value slightly below 3, but still near 3. A calculator level calculation would give around 2.99, which rounds to 3. This confirms that 3 is the closest integer.

Why Other Options Are Wrong:

• 6, 9, and 12 are much larger and would require the numerator to be significantly larger or the denominator much smaller.
• 0 would correspond to a value near zero, which is not reasonable given the approximated numerator of about 21 and denominator near 7.
• Thus 3 is the only option consistent with a reasonable estimate.

Common Pitfalls:

• Failing to convert the percentage correctly to a decimal factor.
• Over rounding the numbers in a way that changes the ratio too much.
• Dividing by the wrong approximate value, such as using 6 instead of about 7, leading to a wrong nearest integer.

Final Answer:
3