For two distinct real numbers x and y, which of them is bigger?

Question

Directions: The question is followed by two statements. Answer using the codes given in the options.

For two distinct real numbers x and y, which of them is bigger?

Statement I: x² < y < 1

Statement II: y < √x < 1

1. A. The question can be answered using one of the statements alone, but cannot be answered using the other statement alone.
2. B. The question can be answered using either statement alone.
3. C. The question can be answered using both the statements together, but cannot be answered using either statement alone.
4. D. The question cannot be answered even using both the statements together. (Correct answer)

Correct Answer

Option D — The question cannot be answered even using both the statements together.

Detailed Solution & Explanation

The correct answer is Option D (cannot be answered even with both statements).

Key Points

• Statement I (x² < y < 1) and Statement II (y < √x < 1) each fail to fix the order of x and y individually.
• Combining them: for 0 < x < 1 we have x² < x < √x, and y lies in the interval (x², √x) — but x also lies in that same interval, so y can be either larger or smaller than x.

Additional Information

• Example: x = 0.25 gives the window (0.0625, 0.5); y could be 0.4 (> x) or 0.1 (< x). The comparison stays undetermined, so Option D.