BTGModeratorVI wrote: ↑Fri Aug 14, 2020 1:07 pm
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
Answer:
B
Source: Official guide
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
