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GATE 2023 IN – Question 3

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

A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

  1. 125
  2. 720
  3. 60
  4. 80

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Show answer and explanation

Correct answer: (D) 80

Explanation

Each digit is chosen from 1, 3, 5, 7, 9. The first has 5 choices; each later digit has 4 choices because only its immediate predecessor is excluded. The first and third may match. Total $5(4)(4)=80$, **D**.