If -1/2 x -1/9 and -1/4 y -1/25 and -1/4 y -1/25, what is

We have -\(\frac{1}{2}\) ≤ x ≤ -\(\frac{1}{9}\) and -\(\frac{1}{4}\) ≤ y ≤ -\(\frac{1}{25}\)

Squaring for y, we get \(\frac{1}{16}\) ≤ \(y^2\) ≤ \(\frac{1}{625}\)

To get \(x * y^2\), we multiply and get all possible values with the endpoints of x and the endpoints of \(y^2\)


The possible values are:

(i) \(x * y^2\) = -\(\frac{1}{2}\) * \(\frac{1}{16}\) = -\(\frac{1}{32}\)

(ii) \(x * y^2\) = -\(\frac{1}{2}\) * \(\frac{1}{625}\) = -\(\frac{1}{1350}\)

(iii) \(x * y^2\) = -\(\frac{1}{9}\) * \(\frac{1}{16}\) = -\(\frac{1}{144}\)

(iv) \(x * y^2\) = -\(\frac{1}{9}\) * \(\frac{1}{625}\) = -\(\frac{1}{5625}\)

Since we want the minimum value and all the values are negative, we for denominator with the least value (if all were positive, we would look for the denominator with the maximum value).

The denominator with the least value is -\(\frac{1}{32}\)

Option D

Arun Kumar