Perform no-calculator math accurately and fast

Without using a calculator, complete each item in at most 90 seconds and briefly describe the mental shortcuts you applied: a) $37 \times 43$; b) $999 \times 997$; c) $65^2$; d) estimate $(1.07)^5$ to within 0.005; e) give tight two-sided bounds for $e^{0.3}$ (explain your bounds); f) $\sqrt{998,001}$.

Overview: This item assesses mental calculation, quick estimation, numerical bounding, and comfort with exponentials and square-root approximations, and it sits in the Statistics & Math category for a Data Scientist position.

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