Which of the following specifies all the possible values of xy

(B) -42 < xy < 24

Go for the extremes in such Qs. We can get a value ~ -42 if x = 6.99999999 and y = -5.99999999

And ~ 24 if x = -3.99999999 and y = -5.99999999

Extreme Points Q

-4 * -6 = 24
7 * - 6 = -42
-4 * 3 = -12
7 * 3 = 21

Therefore, max range = -42 < xy < 24 => B

Minimum value of xy = 7(-6) = -42
Maximum value of xy = (-4)(-6)=24

-42<xy<24

IMO B

Posted from my mobile device

Easier than it looks! Thank you everyone for your help!

Least value of xy is about 7*(-6) = -42
Max. value of xy is about -4*(-6) = 24

--> -42 < xy < 24

IMO Option B

Posted from my mobile device

The question corresponds to the Max-Min Concept of Inequalities.
Whenever two ranges of inequalities are given in x and y and you need to evaluate the value of x + y , x * y, and x – y then use the max-min concept

You can use the following steps to do so:
(1)Place the two inequality ranges one below the other
(2)Make sure the inequality signs are the same in both cases
(3)If the signs are not the same use the properties of inequalities to make them the same
(4)Now add/multiply/subtract both in a straight line and diagonally to get 4 values

->The greatest value will be max and the lowest value will be min
In this question,

-4 < x < 7 and
-6 < y < 3

=>The values on multiplying vertically and diagonally are 24,21,-12,-42 and hence using the concept stated above we have

-42 <xy <24 (option b)

Devmitra Sen
GMAT SME

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