There are four consecutive even integers.Sum of the reciprocals of the first two numberis (11/60). Find the reciprocal of third largestnumber of the series.

There are four consecutive even integers.Sum of the reciprocals of the first two numberis (11/60). Find the reciprocal of third largestnumber of the series. Correct Answer 1\/14

Ans. C.Let 4 consecutive even numbers are x, x+ 2, x+ 4, x+ 6According to the question -1/x + 1/x+2 = 11/60x+2+x/ x(x+2) = 11/602(x+1)/x^2 + 2x = 11/60120x + 120 = 11x 2 + 22x11x 2 - 98x – 120 = 0So ,X = -24/22 , 10X = -12/11 , 10So, the numbers will be 10,12,14,16.Hence,Third largest number = 14Reciprocal of third number = 1/14

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