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NDA 2 2025 Maths, question 7

Topic: Algebra

Q7

How many terms are identical in the two APs 19,21,23,…19,21,23,\ldots up to 110110 terms and 19,22,25,28,…19,22,25,28,\ldots up to 7575 terms?

  1. (a) 3535
  2. (b) 3636
  3. (c) 3737Correct answer
  4. (d) 3838

Solution.

Answer: (c) 3737

  1. The last terms are 19+109×2=237 and 19+74×3=241.
  2. Common terms occur every lcm(2,3)=6, beginning at 19.
  3. Therefore the number is floor((237−19)/6)+1=37; the last common term is 235.