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SSC Selection Post 2022 PYQ — Question 72

SSC Selection Post - Matriculation Level 2022 - 3 Aug 2022 - Shift 1 • Quantitative Aptitude • Q72

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A number is square of 167. When digits of the number are rearranged in descending order, then the new number which is formed will be divisible by:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 17.

The square of 167 is = 1672 = 27889

Rearranging its digits in descending order:

Digits of 27889 = 2, 7, 8, 8, 9 → Descending order = 98872

The alternating sum rule:

  • Alternate sum of digits = 9 − 8 + 8 − 7 + 2 = 4 → Not divisible by 11
  • 98872÷13≈7605.54⇒98872 \div 13 \approx 7605.54 \Rightarrow  Not exact → Not divisible by 13
  • Ends in 2 → Not 0 or 5 → Not divisible by 5
  • 98872÷17=5816⇒98872 \div 17 = 5816 \Rightarrow  Exact division → 98872 is divisible by 17.