There is a question followed by two statements I and II : Question : If x and y are integers, can we find |x-y| uniquely? I. x2 + y2 = 25 II. x2 - y2 = 7 Which one of the following options is correct?

Option D: The question cannot be answered even using any of the statements

CAPF AC 2026 PYQ with Answer — There is a question followed by two statements I and II : Question :…

2026 · Q57

There is a question followed by two statements I and II :

Question :

If x and y are integers, can we find |x-y| uniquely?

Ix2 + y2 = 25
IIx2 - y2 = 7 Which one of the following options is correct?

general-mental-abilityquantitative-aptitude

AThe question can be answered using one of these statements alone, but cannot be answered using the other statement
BThe question can be answered using either statement alone
CThe question can be answered using both the statements together, but cannot be answered using either statement alone
DThe question cannot be answered even using any of the statements

Explanation

From statement I, x² + y² = 25 has several integer solutions — (±5, 0), (0, ±5), (±3, ±4), (±4, ±3) — giving |x − y| values of 1, 5 or 7, so it is not unique. From statement II, x² − y² = 7 gives (x − y)(x + y) = 7, yielding |x − y| of 1 or 7, again not unique. Using both together gives x = ±4, y = ±3, for which |x − y| is still 1 or 7 — not unique. Hence the question cannot be answered even using both statements.