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Part ACSIR NET December 2025match-the-residue-class-mod-3-not-the-nearer-looking-index

Match the residue class mod 3 not the nearer looking index

Suppose a1,a2,…,a300a_{1}, a_{2}, \dots, a_{300} are integers such that aia_{i}₋1+ai+ai_{1} + a_{i} + a_{i}₊1=2025_{1} = 2025 for all i = 2, 3, …, 299. If a7=−5,a9=37a_{7} = -5, a_{9} = 37, then the value of a106a_{106} is

  1. A.1993
  2. B.37
  3. C.−5✓
  4. D.2030

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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