Approximation and quick calculation: Evaluate 3739 + (164 × 27) and choose the closest option.

Introduction / Context:
This checks quick multiplication and addition. Since options are widely spaced, an accurate but mental computation is enough to reach the nearest choice without a calculator.

Given Data / Assumptions:

• Compute 3739 + 164 * 27.
• Pick the closest available option.

Concept / Approach:
Multiply 164 by 27 using a breakup such as 164 * (30 − 3) or (20 + 7) * 164, then add 3739. Because answer choices differ by thousands, a precise integer computation is fast and safest.

Step-by-Step Solution:

Verification / Alternative check:
Compute 164*20 = 3280 and 164*7 = 1148; sum 3280 + 1148 = 4428; add 3739 → 8167. Same result, confirming the nearest option is 8200.

Why Other Options Are Wrong:

• 105400: Off by two orders of magnitude; misread or misplace zeros.
• 4000: Below even the product 164*27; impossible.
• 690: Far smaller than either component.
• None of these: A very close option (8200) exists.

Common Pitfalls:
Misplacing a zero or using 164*30 without subtracting 164*3. Keep track of the compensation step.

Final Answer:
8200