CDS 2026 (I) Elementary Mathematics, question 31

Topic: Number system

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Q31

Let P=N2P=N^{2} where NN is an odd integer. What is the remainder when PP is divided by 88 ?

  1. (a) 11Correct answer
  2. (b) 33
  3. (c) 55
  4. (d) Cannot be determined due to insufficient data

Solution.

Answer: (a) 11

  1. Write N=2k+1N = 2k + 1.
  2. Then N2=4k(k+1)+1N^{2} = 4k(k + 1) + 1.
  3. One of the consecutive integers k and k+1k + 1 is even, so 4k(k+1)4k(k + 1) is divisible by 8.