Inequalities involving Extreme Operators. Pl help understand

[abhistud0554]

Hi,

If -4 < a < 4 and -2 < b < -1, which of the following could NOT be the value of ab ?

A) -3
B) 0
C) 4
D) 6
E) 9

[spoiler]Solution : E.[/spoiler]

[spoiler]Step 1: Extreme values for a are GT(-4) and LT(4).
Extreme values for b are GT(-2) and LT(-1).
GT - Greater Than; LT - Less than

Step 2: Thus from step 1, we can understand that a can be positive or negative while b can only be negative, so ab can be positive and negative.

Step 3: The most negative ab can be is GT(-2)*GT(4) = GT(-8)
The most positive ab can be is GT(-4)*GT(-2)= LT(8)[/spoiler]


Can someone please help me understand step 3? I don't understand how they got the most negative and positive values for a and b individually, and how multiplying 2 extreme values together work when they are not both positive like GT(-2)*GT(4) = GT(-8) or if both are negative GT(-4)*GT(-2)= LT(8)?

[Jim@StratusPrep]

The extreme values came from the numbers in the actual inequality. The smallest A can be is a tiny bit bigger than -4 and the largest it can be is just smaller than 4. You then multiply the extremes to make the smallest and largest numbers possible. If that does not make sense, then study some positive and negative number calculations.

Make sense?

[GMATGuruNY]

Hi,

If -4 < a < 4 and -2 < b < -1, which of the following could NOT be the value of ab ?

A) -3
B) 0
C) 4
D) 6
E) 9

The range of a has two endpoints -4 and 4.
The range of b has two endpoints: -2 and -1.

To determine the range of ab, calculate the value of ab using EVERY POSSIBLE COMBINATION OF ENDPOINTS:
(-4)(-2) = 8.
(-4)(-1) = 4.
(4)(-2) = -8.
(4)(-1) = -4.

The least result is the LOWER BOUNDARY of ab: -8.
The greatest result is the UPPER BOUNDARY of ab: 8.
Thus:
-8 < ab < 8.

Since ab can be any value between -8 and 8, ab can be equal to every answer choice but E.

The correct answer is E.