What approximate value should come in place of the question mark (?) in the expression (55.01 + 16.0003) × 22.01 ÷ 10.998, if you are expected to find a close numerical estimate rather than the exact value?

Introduction / Context:
This problem checks your ability to approximate operations involving decimals. Instead of doing lengthy exact calculations, you are expected to gently round the numbers to convenient values and then compute a close estimate, which is a common technique in time-pressured competitive exams.

Given Data / Assumptions:

• Expression: (55.01 + 16.0003) × 22.01 ÷ 10.998.
• We are looking for a reasonable approximation, not exact arithmetic.
• All numbers are close to convenient integers.

Concept / Approach:
The idea is to round each number to a nearby simple value, as long as the rounding does not introduce too much error. We then perform the simplified operations to get an approximate result. Since the options are well separated, a reasonably good approximation will clearly indicate the correct choice.

Step-by-Step Solution:
Step 1: Approximate 55.01 as 55. Step 2: Approximate 16.0003 as 16. Step 3: Compute the sum inside the brackets: 55.01 + 16.0003 ≈ 55 + 16 = 71. Step 4: Approximate 22.01 as 22. Step 5: Approximate 10.998 as 11. Step 6: Substitute these approximations into the expression: (55.01 + 16.0003) × 22.01 ÷ 10.998 ≈ 71 × 22 ÷ 11. Step 7: First divide: 22 ÷ 11 = 2. Step 8: Multiply: 71 × 2 = 142. Step 9: Therefore, the approximate value is about 142.

Verification / Alternative check:
Because all the original decimals are extremely close to the integers we used (differences are around 0.01 or less), the resulting product and quotient will not deviate much from our approximate result. A more precise calculation would yield a value very close to 142, confirming that 142 is the best available approximation among the choices.

Why Other Options Are Wrong:
Values like 190 or 160 are significantly higher than our estimate, and 130 or 110 are noticeably lower. Since our approximations are very tight and involve only minimal rounding, any large deviation from 142 is not justified by the arithmetic.

Common Pitfalls:
Some students try to perform full precise calculations, which is time consuming. Others incorrectly round in a way that changes the structure of the expression, such as rounding both numerator and denominator in opposite directions. A balanced rounding, where all numbers are rounded sensibly to the nearest simple values, produces an accurate estimate efficiently.

Final Answer:
The approximate value of the expression is 142.