In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q - S = 2S and T = R + S + 3, then what is the value of P + R - T?

(a) 1
(b) 2 ✓ UPSC's answer
(c) 3
(d) Cannot be determined due to insufficient data

Why the answer is (b)

• The equation Q - S = 2S simplifies to Q = 3S.

• From the set {4, 5, 10, 12, 15}, the only pair where one number is three times the other is S = 5 and Q = 15.

• Substituting S = 5 into T = R + S + 3 gives T = R + 8.

• The remaining numbers are {4, 10, 12}. The only pair where the difference is 8 is R = 4 and T = 12.

• This leaves P = 10 as the only remaining number.

• Calculating P + R - T yields 10 + 4 - 12 = 2.

Why the other options are wrong

(a) 1: The calculated value is 2, not 1, based on the unique assignment of numbers to letters.
(c) 3: The calculated value is 2, not 3, as derived from the specific values P=10, R=4, and T=12.
(d) Cannot be determined due to insufficient data: The data is sufficient to uniquely determine the values of all letters, so the answer is determinable.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.