5 lb. Book of GRE Chapter 11 Question 38

GRE Quant Problem Solving
1

Question: The reciprocal of x’s non-integer decimal part equals x + 1, and x > 0.
Quantity A: x
Quantity B:sqrt(2)
Answer: C
However, to prove the answer, the book assumes that x = sqrt(2), and reaches the conclusion from there that A = B. But how can we know that this does not work for another x != 2? In other words, that D is the answer?

Many thanks!

2

You’re right, and the question appears to be faulty. See The reciprocal of x’s non-integer decimal part equals x + 1, : Quantitative Comparison Questions