Without detailed exact computation, estimate the value of sqrt(3099.985 ÷ 62.001 + 14.001) and choose the closest integer answer from the options provided.

Introduction / Context:
This question focuses on estimation with square roots and division. Many aptitude exams include similar problems where the numbers are slightly perturbed from nice values, so you must recognize patterns and approximate efficiently without detailed calculator style arithmetic.

Given Data / Assumptions:

• The expression is sqrt(3099.985 ÷ 62.001 + 14.001).
• We are asked to find the closest integer to this value.
• The numbers are very close to 3100, 62, and 14 respectively, suggesting an underlying neat value.

Concept / Approach:
We approximate the division 3099.985 ÷ 62.001 by using nearby round numbers. Then we add the approximate 14.001 and finally take the square root of the resulting sum. Recognizing that perfect squares such as 64 equal 8^2 is helpful in estimating the square root quickly and matching it with the closest integer option.

Step-by-Step Solution:
Approximate 3099.985 as 3100 and 62.001 as 62 for easier computation.Compute the approximate division: 3100 ÷ 62 is very close to 50 because 62 × 50 = 3100.Now add the approximate 14.001, which is very close to 14. So the expression inside the square root is about 50 + 14 = 64.Compute the square root: sqrt(64) = 8.Therefore, the value of the original expression is very close to 8, so the nearest integer is 8.

Verification / Alternative check:
If we perform a more precise calculation, the division 3099.985 ÷ 62.001 gives a value very slightly less than 50, and adding 14.001 produces a result very close to 64. The square root of a number extremely close to 64 will be extremely close to 8. The tiny differences do not change the nearest integer, confirming that 8 is the correct choice.

Why Other Options Are Wrong:

• 13, 18, and 23 correspond to squares 169, 324, and 529 respectively, which are far away from the inside value around 64.
• 10 would require the inside expression to be near 100, which is much larger than our approximate 64.
• Thus, only 8 is consistent with a square root near 64.

Common Pitfalls:

• Failing to recognize that the numbers are designed to produce a value very close to 64 inside the square root.
• Incorrectly approximating the division by using an overly rough guess such as 40 or 60.
• Forgetting to add the extra 14 before taking the square root, which drastically changes the result.

Final Answer:
8