Find the minimum possible value of 'y' if \frac{4}{7}

CAT 2016 Quantitative Ability

Question : 16 of 34

Marks: +1, -0

Find the minimum possible value of 'y' if

\;\;{4}/{7}<\;\;{x}/{y}<\;\;{12}/{13},

where x and y are natural numbers

Solution:

\;\;{4}/{7} < {x}/{y} < {12}/{13},

⇒ {13x}/{12} < y< {7x}/{4}

As ‘x’ increases, the interval in which ‘y‘ lies alsoincreases.
For x = 1, the intervals in which y lies is

(1 {1}/{12},1 {3}/{4})

This interval does not contain any integer.
For x = 2, the interval in which y lies is

(2 {1}/{6},3 {1}/{2})

and 3 lies in the interval.
Hence, the minimum possible value of y is 3.

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