Q:
      
      
         
            
There are four consecutive even integers. Sum of the reciprocals of the first two number is (11/60). Find the reciprocal of third largest number of the series.
         
       
      
      
      
          
      
      
          Answer & Explanation
         Answer: C) 1/14         
         
Explanation: Ans. C.
Let 4 consecutive even numbers are x, x+ 2, x+ 4, x+ 6
According to the question -
1/x + 1/x+2 = 11/60
x+2+x/ x(x+2) = 11/60
2(x+1)/x^2 + 2x = 11/60
120x + 120 = 11x 2 + 22x
11x 2 - 98x – 120 = 0
So ,
X = -24/22 , 10
X = -12/11 , 10
So, the numbers will be 10,12,14,16.
Hence,
Third largest number = 14
Reciprocal of third number = 1/14
       
      
      
      
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