Question

The instructions below apply to this question and the previous one.

In the figure below, the seven letters correspond to seven unique digits chosen from 0 to 9. The relation among the digits is such that:

\(P \times Q \times R = X \times Y \times Z = Q \times A \times Y\)

P		X
Q	A	Y
R		Z

The sum of the digits which are not used is:

• A. 8
• B. 10
• C. 14
• D. None of the above

Hint:

Once the seven used digits are pinned down from the previous question's working, list which digits from 0 to 9 are left over and add them up.

Answer 1

The Correct Option is D

Step 1: Recall the digits used.
From the previous question, one valid, consistent assignment satisfying \(P \times Q \times R = X \times Y \times Z = Q \times A \times Y\) is:
\(A = 2\), \(Q = 9\), \(Y = 4\), \(\{P, R\} = \{1, 8\}\), \(\{X, Z\} = \{3, 6\}\), all giving a common product of 72.
The seven digits used are: 1, 2, 3, 4, 6, 8, 9.

Step 2: Find the digits left over.
Out of all ten digits from 0 to 9, the ones not among \(\{1, 2, 3, 4, 6, 8, 9\}\) are: 0, 5 and 7.

Step 3: Add up the unused digits.
\[ 0 + 5 + 7 = 12 \]

Step 4: Compare with the options.
The sum 12 does not match 8, 10, 14 or 15, the four numeric choices offered.

Final Answer:
Since the true sum of unused digits is 12, which is not among the listed numeric options, the correct choice is None of the above.
\[ \boxed{\text{None of the above}} \]