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?

1. A. 1
2. B. 2
3. C. 3
4. D. Cannot be determined due to insufficient data

Answer: B

Explanation

This question involves logical deduction and algebraic manipulation, typical for CSAT’s analytical reasoning section. The given numbers are {4, 5, 10, 12, 15}.
From the first equation, Q – S = 2S, we get Q = 3S. We look for pairs in the given numbers where one is three times the other. The only possible pair is S=5 and Q=15.
Now, substitute S=5 into the second equation: T = R + S + 3, which becomes T = R + 5 + 3, so T = R + 8.
The remaining numbers are {4, 10, 12}. We need to find R and T from these such that T = R + 8.
If R=4, then T = 4 + 8 = 12. This is a valid assignment as both 4 and 12 are in the remaining numbers.
So, we have S=5, Q=15, R=4, T=12. The only number left is 10, so P=10.
Finally, calculate P + R – T = 10 + 4 – 12 = 14 – 12 = 2. This problem assesses systematic problem-solving and logical consistency.