XY

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 kamalakarthi,

I think that Brent accidentally posted an answer to a different question here.

For this question, we have two ranges of values to consider:

-4 < X < 7
-6 < Y < 3

And we're asked for the range of XY. To properly answer this question, we have to be sure that we've found the lowest and highest possibilities.

From the answer choices, we can tell that the least possible number is a negative value, but HOW negative can we get…. Multiplying two values together and ending with a negative product means that one value will be positive and one will be negative….

Looking at the "extreme" possibilities in the two ranges, that product would be (7)(-6) = -42

So -42 < XY

Now we have to go after the highest value, which will mean EITHER multiplying two positive values OR two negative values.

The possibilities are…
(7)(3) = 21
(-4)(-6) = 24

Since 24 is bigger, that value is our maximum.

The final range is….

-42 < XY < 24

Final Answer: B

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

Thanks Rich - I wasn't paying attention.

I've fixed my post.

Cheers,
Brent