Discussion
This question is followed by two statements A and B. Indicate your responses based on the given choices.
Is x greater than y?
Statement A: x is twice of 10 more than z.
Statement B: y is twice of 10 less than z.
Answer: C
The question can be answered using statements A and B together but not by either statement alone.
Statement A ties x to z, \(x = 2(z + 10)\); statement B ties y to z, \(y = 2(z - 10)\). Alone, each says nothing about the other variable, so neither is sufficient.
Together:
\[ \begin{aligned} x - y &= 2(z + 10) - 2(z - 10) \\ &= 40 \gt 0 \end{aligned} \]
so x is greater than y whatever z is. The same holds if the statements are read as \(x = 2z + 10\) and \(y = 2z - 10\), where the difference is 20.
The 'A alone' and 'B alone' options fail because each statement mentions only one of x and y. The last option fails because the two together do settle the question.
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