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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 _____.

  1. $1/12$
  2. $1/8$
  3. $1/6$
  4. $3/8$ 
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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 = $\frac{1}{4}\times \frac{3}{2}=\frac{3}{8}$

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