How to approach these kind

If -4 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?

a. -42<xy<21
b. -42<xy<24
c. -28<xy<18
d. -24<xy<21
e. -24<xy<24

Let's examine the EXTREME VALUES Of x and y and see what happens.

If we want to MINIMIZE the value of xy, we need to examine what happens when 1 EXTREME value is positive and 1 EXTREME value is negative.
case a: x = -4 and y = 3, in which case xy = -12
case b: x = 7 and y = -6, in which case xy = -42
Great, so xy is MINIMIZED when x = 7 and y = -6
Of course, we're told that x < 7 and y > -6, but that's fine. Basically, this means that xy > -42

At this point, we know that the correct answer must be either A or B.

Next, if we want to MAXIMIZE the value of xy, we need to examine what happens when both EXTREME values are positive or both are negative.
case c: x = -4 and y = -6, in which case xy = 24
case d: x = 7 and y = 3, in which case xy = 21
Great, so xy is MAXIMIZED when x = -4 and y = -6
Of course, we're told that x > -4 and y > -6, but that's fine. Basically, this means that xy < 24

So, as you can see, -42 < xy < 24

Answer: B

Cheers,
Brent

Hi phanikpk,

This question is built around "Number Properties" - the "little rules" around which all math is built.

We're dealing with the following Number Properties in this question:
(Positive) x (Positive) = Positive
(Negative) x (Negative) = Positive
(Positive) x (Negative) = Negative

We're also dealing with the idea of minimums and maximums, so we have to think about the smallest and biggest possibilities given the restrictions in the question.

The big "quirk" in this question is that you actually have to multiply to the two most extreme NEGATIVE possibilities to find the largest POSITIVE product. More than anything else, this question is testing your thoroughness and attention to detail, since the math is just basic multiplication.

GMAT assassins aren't born, they're made,
Rich