Consider the following statements I. There exists a natural number which when increased by 50% can have its number of factors unc…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

Consider the following statements:

I. There exists a natural number which when increased by 50% can have its number of factors unchanged.

II. There exists a natural number which when increased by 150% can have its number of factors unchanged.

Which of the statements given above is/are correct?

  1. A. I only
  2. B. II only
  3. C. Both I and II (Correct answer)
  4. D. Neither I nor II

Correct Answer

Option C — Both I and II

Detailed Solution & Explanation

The correct answer is Both I and II.

Key Points

  • Statement I: Increase a number by 50%: e.g., 2 → 3. Factors of 2: {1,2} = 2 factors.
  • Factors of 3: {1,3} = 2 factors. ✓ Same number of factors. I is correct.
  • Statement II: Increase by 150%: multiply by 2.5. e.g., 4 → 10. Factors of 4: {1,2,4} = 3. Factors of 10: {1,2,5,10} = 4. Try 2→5: factors of 2=2, factors of 5=2. ✓ II is correct. Answer: Both I and II.