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GATE 2024 CE (CE1) – 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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Show answer and explanation

Correct answer: (D) 31

Explanation

The terms are one less than powers of two: $3 = 2^2 - 1$, $7 = 2^3 - 1$, $15 = 2^4 - 1$, so $x = 2^5 - 1 = 31$, followed by $63 = 2^6 - 1$, $127 = 2^7 - 1$ and $255 = 2^8 - 1$.