GATE Electrical 2019 | GA | Question: 9

Question

Given two sets $X=\{1,2,3\}$ and $Y=\{2,3,4\},$ we construct a set $Z$ of all possible fractions where the numerators belong to set $X$ and the denominators belong to set $Y.$ The product of elements having minimum and maximum values in the set $Z$ is _____.

• A. $1/12$
• B. $1/8$
• C. $1/6$
• D. $3/8$ 

Comments

The value will be maximum when the numerator is the highest from the x set and the denominator is the lowest from the y set, and minimum when the numerator is the lowest from the x set and the denominator is the highest from the y set.

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don't made the mistake of taking minimum as 1/2 and maximum as 3/4.

Answer 1

Answer D.

For minimum value pick the smallest value from $X$ as numerator and largest value from $Y$ as denominator
$\implies $Minimum value $=\frac{1}{4}$

For maximum value pick the largest value from $X$ as numerator and smallest value from $Y$ as denominator
$\implies$ Maximum value $=\frac{3}{2}$

Their product = $\frac{1}{4}\times \frac{3}{2}=\frac{3}{8}$