Instructions: A numerical machine accepts two values X and Y. At every step, it updates the values as X = X times Y, and Y = Y + 1. The machine stops as soon as X becomes greater than or equal to N.

Starting again from X = 3, Y = 2, if the value of N is changed to 500, what would be the final value of X?

Question

Which number comes next in the series? 3, 6, 11, 18, 27, ?

Answer 1

Raising N from 100 to 500 only matters if X = 360 (the value that satisfied the old N) is still below the new threshold, so we check that first.

360 is less than 500, so the machine does not stop at step 4 this time and must continue.
Step 5 multiplies X by the current Y (6): $360 \times 6 = 2160$, and Y becomes 7.
2160 is well past 500, so the machine halts at this step.

So the final value of X, once N is raised to 500, is 2160.

The correct answer is option D.

Answer 2

Raising N from 100 to 500 only matters if X = 360 (the value that satisfied the old N) is still below the new threshold, so we check that first.

360 is less than 500, so the machine does not stop at step 4 this time and must continue.
Step 5 multiplies X by the current Y (6): $360 \times 6 = 2160$, and Y becomes 7.
2160 is well past 500, so the machine halts at this step.

So the final value of X, once N is raised to 500, is 2160.

The correct answer is option D.

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