Question : The sum of a two-digit number and the number obtained by reversing its digits is a square number. How many such numbers are there?
Option 1: 5
Option 2: 6
Option 3: 7
Option 4: 8
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Correct Answer: 8
Solution :
Let the digits be x and y respectively. So, the number will be = 10x + y Given: (10x + y) + (10y + x) = Square Number ⇒ 11( x + y ) = Square Number ⇒ 11( x + y ) = 121 ( Only possible square number ) ⇒ x + y = 11 Possible combination of (x,y) = (2,9) (3,8) (4,7) (5,6) (6,5) (7,4) (8,3) (9,2). So, the total possible combinations are 8. Hence, the correct answer is 8.
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