Passage

Directions for the following 5 (five) items : Each item in this section contains a question followed by two statements. Answer each item using the following instructions and mark your response on the Answer Sheet accordingly. (a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement (b) Select this option if the question can be answered using either statement alone (c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone (d) Select this option if the question cannot be answered even using any of the statements

Question : For two distinct real numbers x and y, which of them is bigger? Statement I : x² < y < 1 Statement II : y < √x < 1

(a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
(b) Select this option if the question can be answered using either statement alone
(c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
(d) Select this option if the question cannot be answered even using any of the statements ✓ UPSC's answer

Why the answer is (d)

• Statement I (x² < y < 1): take y = 0.3. With x = 0.5 (x² = 0.25) x is bigger; with x = 0.1 (x² = 0.01) y is bigger. Not sufficient.

• Statement II (y < √x < 1): take x = 0.25, so √x = 0.5. With y = 0.3 y is bigger; with y = 0.1 x is bigger. Not sufficient.

• Both together (x² < y < √x < 1): x = 0.25 needs 0.0625 < y < 0.5. Both y = 0.1 (x bigger) and y = 0.3 (y bigger) satisfy every condition.

• Since the comparison still changes, even both statements together cannot answer the question: (d).

Why the other options are wrong

(a) Select this option if the question can be answered using one of these statements alone…: Neither statement alone fixes which number is bigger; counter-examples exist for each.
(b) Select this option if the question can be answered using either statement alone: Neither statement alone is sufficient.
(c) Select this option if the question can be answered using both the statements together…: Even together, x = 0.25 with y = 0.1 or y = 0.3 gives opposite answers.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.