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Q57 (CAPF/2026) Miscellaneous & General Knowledge › Important Days, Places & Events

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?

Result
Your answer: —  ·  Correct: D

Explanation

To determine if |x - y| can be found uniquely, we evaluate the statements provided:

Statement I: x2 + y2 = 25. Since x and y are integers, possible pairs (x, y) include (5, 0) and (3, 4). For (5, 0), |x - y| = 5. For (3, 4), |x - y| = 1. Since multiple values are possible, Statement I alone is not sufficient.

Statement II: x2 - y2 = 7. This can be factored as (x - y)(x + y) = 7. Since x and y are integers, the factors of 7 are (1, 7), (7, 1), (-1, -7), and (-7, -1).
If (x - y) = 1 and (x + y) = 7, then x = 4, y = 3, and |x - y| = 1.
If (x - y) = 7 and (x + y) = 1, then x = 4, y = -3, and |x - y| = 7.
Since |x - y| can be 1 or 7, Statement II alone is not sufficient.

Combined: Solving both equations simultaneously gives x2 = 16 and y2 = 9, resulting in x = ±4 and y = ±3. The possible values for |x - y| remain 1 and 7. Because the value is not unique, the question cannot be answered even using both statements.

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