Question:
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.
If X = 2 and Y = 3, what should be the minimum value of N (from the options given) such that the final value of Y is 7?
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.
If X = 2 and Y = 3, what should be the minimum value of N (from the options given) such that the final value of Y is 7?
If X = 2 and Y = 3, what should be the minimum value of N (from the options given) such that the final value of Y is 7?
Show Hint
Y reaches 7 only if the machine stops exactly at step 4, which needs N strictly above 120 and at most 720.
Updated On: Jul 15, 2026
- 300
- 360
- 720
- 860
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The Correct Option is A
Solution and Explanation
Step 1: Run the machine starting from X = 2, Y = 3.
Step 1: X = 2 x 3 = 6, Y = 4.
Step 2: X = 6 x 4 = 24, Y = 5.
Step 3: X = 24 x 5 = 120, Y = 6.
Step 4: X = 120 x 6 = 720, Y = 7.
Step 2: Find the range of N that makes the machine stop exactly at this step.
For the final Y to be exactly 7, the machine must stop right after step 4, meaning X must first reach or cross N at step 4 (X = 720) but not earlier (X was only 120 after step 3). So N must satisfy \(120 < N \le 720\).
Step 3: Check the given options against this range.
300, 360 and 720 all fall inside \(120 < N \le 720\), while 860 is above 720 and would let the machine run one more step (to Y = 8), so it is excluded.
Step 4: Find the minimum valid value.
Among 300, 360 and 720, the smallest is 300.
Step 5: Final Answer.
The minimum value of N among the choices that still gives a final Y of 7 is 300, so option A is correct.
Step 1: X = 2 x 3 = 6, Y = 4.
Step 2: X = 6 x 4 = 24, Y = 5.
Step 3: X = 24 x 5 = 120, Y = 6.
Step 4: X = 120 x 6 = 720, Y = 7.
Step 2: Find the range of N that makes the machine stop exactly at this step.
For the final Y to be exactly 7, the machine must stop right after step 4, meaning X must first reach or cross N at step 4 (X = 720) but not earlier (X was only 120 after step 3). So N must satisfy \(120 < N \le 720\).
Step 3: Check the given options against this range.
300, 360 and 720 all fall inside \(120 < N \le 720\), while 860 is above 720 and would let the machine run one more step (to Y = 8), so it is excluded.
Step 4: Find the minimum valid value.
Among 300, 360 and 720, the smallest is 300.
Step 5: Final Answer.
The minimum value of N among the choices that still gives a final Y of 7 is 300, so option A is correct.
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