UPPSC PCS - 2015

Three of the following four pairs of numbers have the same relationships. Select the odd pair out.

Year Asked: 2015

A
4 :63
B
1 : 0
C
5 :124
D
2 : 9

Correct Answer

D. 2 : 9

Detailed Explanation

The rule linking each pair is that the second number is the cube of the first minus one: second = n³ − 1. Test it on every option.

  • A) 4 : 63 fits, since 4³ − 1 = 64 − 1 = 63.
  • B) 1 : 0 fits, since 1³ − 1 = 0.
  • C) 5 : 124 fits, since 5³ − 1 = 125 − 1 = 124.
  • D) 2 : 9 breaks the rule. 2³ − 1 = 7, not 9. The value 9 is 2³ + 1, which is the wrong sign.

So D is the odd pair out. This is a standard number-pair or series question from the reasoning and aptitude part of the exam. Its Mains link is thin, but the habit of testing one clean formula against every pair is what carries over to data-interpretation and quantitative questions.

Trap: aspirants see 2 : 9 and try a complicated rule like 2×4+1, or assume the pattern is n² based. Test the simplest candidate formula on all four pairs before you look for anything else.

This question appeared in UPPCS 2015 GS Paper 2.

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