If there is a policy that 1/3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period?

1. **Understand the Change**: The question asks for the 'leftover' population. A 2015 PYQ taught us the 'Concept of a Whole and Remainder': if 1/3rd is removed (migrated), then 1 - 1/3 = 2/3rd remains [16].\n\n2. **Apply Recursively**: This migration happens 'every year' for 6 years. This is a 'Successive Fraction Change', similar to the 2014 Net Effect question [7]. We must multiply the remaining factor (2/3) by itself 6 times.\n - Remaining Population = (2/3) × (2/3) × (2/3) × (2/3) × (2/3) × (2/3) = (2/3)^6.\n\n3. **Smart Calculation (Powers of 2)**: We need to find the value of 2^6 / 3^6. A 2016 PYQ on probability emphasized 'Fluency with Powers of 2' [32].\n - Let's just check the top number (Numerator): 2^6.\n - We know 2^5 = 32.\n - Therefore, 2^6 = 32 × 2 = 64.\n\n4. **Check Options**: Look for an option with 64 in the numerator.\n - (A) 16\n - (B) 32\n - (C) 32\n - (D) 64\n\nOnly option (D) matches. We do not need to calculate 3^6 (which is 729), saving time.