Hi all,

As we are looking for the minimum of x*y^2, let's first think about how we can get this for y and x (and the overall). We know that all numbers are negative and the multiplication will be negative because y will always be positive (then we need to look for the greatest value in absolute terms, as it is negative, the greatest one in absolute terms will be the one more "on the left" of the lines of numbers

x: we need the greatest number -> this is x=-1/2
y: we need the greatest number -> this is y=-1/4

Then -1/2*(-1/4)^2 = -1/(2^5)= -1/32

Answer D

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
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CrackverbalGMAT chetan2u Bunuel
I solved this question correctly when I multiplied x by y^2, but not when I multiplied xy by y.
Can you help me understand what's wrong with the second approach?

When we multiply something with y^2, we do not have to change sign because y^2 can never be negative.
However, since we do not know sign of y, multiplication with y can result in different answers.

If y>0, you do not change sign. However, y<0 means change in sign.
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Thank you chetan2u

Does this mean I can't get an answer by multiplying x and y or does it simply mean it's too complicated to even try?

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The easiest way is straight away find out is it negative or positive, if its negative then smaller number is the bigger number, and then sum them up

Posted from my mobile device

In case, you do not know the sign, it is best to avoid multiplication. Of course, you can proceed ahead by testing the inequality considering the variable once as positive and then negative. But it is better avoided that way as there would be better ways to solve the inequality.
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