Let $x$ and $y$ be two different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of $x + y$ is

10

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11

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12

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13

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Solution

The correct option is D $11$
$L e t t h e t w o d i g i t n u m b e r h a s x & y a s t e n s a n d u n i t d i g i t r e s p e c t i v e l y . T h e n t h e n u m b e r i s 10 x + y . S o i t s r e v e r s e n u m b e r i s 10 y + x . A d d i n g, w e g e t t h e s u m = S = (10 x + y) + (10 y + x) ⟹ S = 11 x + 11 y = 11 (x + y) . ∴ T o m a k e S a s q u a r e n u m b e r t h e l e a s t v a l u e o f (x + y) s h o u l d b e 11 s o t h a t S = 11 \times 11 w h i c h i s a s q u a r e n u m b e r . ∴ (x + y) = 11. A n s - O p t i o n B .$

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