GATE 2026 PI – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

Seven bulbs are arranged in a line as shown. All state changes in each step use states at the end of the previous step: an OFF bulb with exactly one ON neighbor turns ON; an ON bulb with both neighbors ON turns OFF; other bulbs remain unchanged. The initial state and steps 1,2 are shown. How many bulbs are ON after step 8?

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Correct answer: (B) 4

Explanation

Write ON as 1 and OFF as 0, reading the figure’s legend carefully. Initial state is 0001000. Simultaneous updates give step 1: 0011100; step 2: 0110110; step 3: 1110111; step 4: 1010101. In the last state, each OFF bulb has two ON neighbors and each ON bulb lacks two ON neighbors, so no rule changes any bulb. It remains fixed through step 8, with **four ON bulbs, B**.

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