Approximation and quick calculation: Evaluate (21 + 99) × (30 − 19.02) and select the closest option.

Difficulty: Easy

Correct Answer: 1290

Explanation:


Introduction / Context:
This problem mixes a clean integer sum with a near-integer difference. Sensible rounding turns it into one quick multiplication. The options are spaced by large gaps, so a tight estimate identifies the correct choice.


Given Data / Assumptions:

  • (21 + 99) = 120
  • (30 − 19.02) ≈ 10.98
  • Compute 120 * 10.98 approximately.


Concept / Approach:
Multiply 120 by 11 and subtract 120 * 0.02. This avoids full decimal multiplication and produces a near-exact result suitable for matching to options.


Step-by-Step Solution:

30 − 19.02 = 10.98 120 * 10.98 = 120 * (11 − 0.02) = 1320 − 2.4 = 1317.6 Nearest listed integer choice is 1290 (difference ≈ 27.6).


Verification / Alternative check:
Exact multiplication confirms 1317.6. Since the next higher provided choice 3581 is far off and 131 is an order of magnitude too small, 1290 is the closest available.


Why Other Options Are Wrong:

  • 3581: Way too large.
  • 131: Ten times too small relative to 1317.6.
  • None of these: Although 1318 would be exact rounding, 1290 is the closest provided choice.


Common Pitfalls:
Multiplying 120 by 11 without subtracting the small correction for 0.02 leads to 1320, still closer to 1290 than any other option but slightly less precise than 1318.


Final Answer:
1290

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