UPSC CAPF AC 2025 Paper 1 · Question 67

Question 67 of the UPSC CAPF (AC) 2025 Paper I (3 August 2025). Try it first, then open the answer and explanation.

1. CAPF 2025 · P-I · Q67 · General Mental Ability · Numbers & Series

   The sum of two numbers is 168. If their HCF is 14, how many such pairs of numbers are possible?

   1. 1
   2. 2
   3. 3
   4. 0

   दो संख्याओं का योगफल 168 है। यदि उनका HCF 14 है, तो संख्याओं के ऐसे कितने युग्म संभव हैं?

   1. 1
   2. 2
   3. 3
   4. 0
   Show answer

   Answer: (2) 2

   उत्तर: (2) 2

   Write the numbers as 14m and 14n with m and n co-prime: 14(m + n) = 168, so m + n = 12. The only co-prime pairs are (1, 11) and (5, 7), since (2, 10), (3, 9), (4, 8) and (6, 6) share a factor, so there are 2 pairs: (14, 154) and (70, 98).

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