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Let $\text{P, Q, S, R, T, U}$ and $\text{V}$ represent the seven distinct digits from $0$ to $6$, not necessarily in that order. If $\text{PQ}$ and $\text{RS}$ are both two-digit numbers adding up to the three-digit number $\text{TUV}$, find the value of $\text{V}$.

  1. $3$
  2. $6$
  3. $5$
  4. Cannot be determined
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2 Answers

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cannot be determined
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Given that PQ + RS = TUV

We have two 2-digit numbers adding up to form a 3-digit number. The only possible values for V, considering the constraints of the problem, are those that result in a carry from the tens to the hundreds place when adding PQ and RS. The digits from 0 to 6 are available, then the only possibilities for V are 0, 1, 2, and 3.

However, without further information, it is impossible to determine the exact value of V. Hence, the answer is "Cannot be determined".

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