#Numbers-10

Consider four-digit numbers for which the first two digits are equal and the last two digits
are also equal. How many such numbers are perfect squares?

(1) 3 (2) 2 (3) 0 (4) 1


Solutions:-

 N=xxyy                                              
N=1000x+100x+10y+y

 =1100x+11y

 11(100x+y)

 (100x+y) will be of the form     x 0 y

  ex:- (100*3 +4)= 3 0 4
                            x 0 y

  For a number to be divisible by 11 difference of (sum of Unit's digit-sum of tens digit ) must be 0,11

 x + y =11
y=11-x

 11(100x + 11- x)
121(9x+1)

 9x+1 will be a perfect sqaure when x=7
                                                         y=4

 Ans:- Option 4  







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