If –12 < x < –2 and 3 < y < 6, which of the following could equal xy ?

This question tests you on the max/min concept of inequalities. Knowing this process will help you avoid falling for obvious traps and give a structured process of working. The two explanations above do not seem to be right as they assume that x and y here are integers. This is a very obvious trap that any test taker will need to avoid.

Let us first discuss the when and how to use the max/min concept of inequalities:

When to use the Max/Min Concept of Inequalities:

Whenever you encounter a question with two finite ranges (x and y in this case) and the question asks us to find the sum (x+y), difference (x-y) and product (xy) of the two ranges, then this concept needs to be used

How to use the Max/Min Concept of Inequalities:

1. Place the two finite ranges one below the other
2. Make sure the inequality signs are the same. If they are not the same then we make them the same by flipping one finite ranges inequality sign. This can be done by reversing the inequality or multiplying throughout by -1
3. Perform the mathematical operation only between the extreme values of the finite ranges.

The question here clearly has two finite ranges and asks us information about the product xy, so we can definitely use the Max/Min concept.

Going step by step

1. Place the two finite ranges one below the other

-12 < x < -2
3 < y < 6

2. Make sure the inequality signs are the same.

The inequality signs are the same here, so we can directly proceed to step 3

3. Perform the mathematical operation only between the extreme values of the finite ranges

-12 < x < -2
3 < y < 6

Multiplying all extreme values in a straight line and cross pattern we get:

-12 * 3 = -36
-2 * 6 = -12
-12 * 6 = -72 (min)
-2 * 3 = -6 (max)

The advantage of the Max/Min concept is that it helps us get the maximum and minimum possible products, hence giving us a range for xy.

Since -6 is the max value and -72 is the min value, the range of xy will be -72 < xy < -6.

Notice here that we are not including -72 and -6 in the range of xy as the original ranges of x and y only have the less than sign and not the less than or equal to.

Now since -72 < xy < -6, the only possible value here for xy will be -71.

Answer: B

For more such Inequality properties, you can go through the following blog

https://www.crackverbal.com/gmat-inequalities/

Hope this helps!

Aditya
CrackVerbal Academic Team