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GATE 2024 XH2 (English) – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Which one of the given options is a possible value of x in the following sequence?

3, 7, 15, x, 63, 127, 255

  1. 35
  2. 40
  3. 45
  4. 31

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Correct answer: (D) 31

Explanation

Each term is one less than a power of 2: 3 = 2² − 1, 7 = 2³ − 1, 15 = 2⁴ − 1, so x = 2⁵ − 1 = 31, followed by 63, 127 and 255. Each term is also twice the previous term plus 1.