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The Executive Assessment (EA) includes inequality questions in the Quantitative Reasoning section, using Problem Solving and Data Sufficiency question formats. These questions test your ability to compare expressions, evaluate solution sets, and apply logical reasoning. You don’t need advanced math; just a strong command of algebra, number properties, and inequality rules is sufficient. By practicing common patterns and avoiding traps, you can master EA inequality problems and boost your Quant score.
Keep reading to learn the types of inequality questions on the EA, step-by-step solving techniques, and tips to avoid common mistakes.
Here are the topics we’ll cover:
- What Are Inequalities?
- Solving Basic Inequalities
- Multiplying or Dividing an Inequality by a Negative Number
- Multiplying or Dividing an Inequality by a Variable — Caution!
- Compound Inequalities
- Summary: EA Inequalities Questions
- What’s Next?
Before jumping into Executive Assessment Quantitative Reasoning inequality questions, let’s discuss some basic inequality concepts.
What Are Inequalities?
An equation shows that 2 expressions are equal, while an inequality shows that they are not. To express inequalities, we use the “greater than” symbol (>) or the “less than” symbol (<).
For example:
- x = 6 is an equation stating that x equals 6.
- x > 10 is an inequality indicating that x can be any value larger than 10.
- x < –2 is an inequality indicating that x can be any value smaller than –2.
KEY FACT:
An inequality compares 2 expressions without asserting equality.
Inequalities can also include “less than or equal to” (≤) and “greater than or equal to” (≥). For instance, x ≤ 14 or x ≥ –8 are both valid inequalities. The same methods and rules for solving EA algebra inequalities also apply when using the “greater than or equal to” or “less than or equal to” symbols.
Let’s now look at some examples and get some Executive Assessment inequalities practice.
Solving Basic Inequalities
Equations and basic linear inequalities are solved in the same way, so there is no big leap in moving from one to the other. When solving for a variable or expression, we use the same algebraic techniques to isolate the variable. The main difference lies in the solution: an equation produces a specific solution, such as x = 3, while an inequality produces a range of solutions such as x > 2, which we can represent on a number line, as displayed below. So, when solving inequalities on the Executive Assessment Quant section, you can basically use the rules you learned for solving equations.
Let’s solve an example of a basic inequality.
Example 1: Solving a Basic Inequality
What is the solution to 2(8x – 6) + 4 ≤ 40?
- x ≥ -3
- x ≤ -3
- x = 3
- x ≤ 3
- x ≥ 3
Solution:
We will solve this inequality using the same algebraic steps as we would for solving an equation. Our goal is to isolate x:
2(8x – 6) + 4 ≤ 40
2(8x – 6) ≤ 36
16x – 12 ≤ 36
16x ≤ 48
x ≤ 3
The solution set x ≤ 3 means that x can be 3 or any number smaller than 3. On a number line, this is shown with a solid circle at 3 and an arrow extending to the left.
Answer: D
TTP PRO TIP:
When solving inequalities, you can follow the same steps you use when solving algebraic equations.
Multiplying or Dividing an Inequality by a Negative Number
Now we are moving deeper into inequalities, and here’s an important twist. While many inequalities are solved just like equations, there’s 1 key exception: whenever you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. This is one of the major EA inequality rules that you must memorize.
For example, consider the inequality:
-3x ≥ 9
To solve, we divide both sides by -3. Since we are dividing by a negative, the inequality sign flips:
x ≤ 9/-3
x ≤ -3
So, the solution set is all values of x less than or equal to -3.
KEY FACT:
When an inequality is multiplied or divided by a negative number, the inequality sign must be reversed.
You may wonder why we have to reverse the inequality sign when multiplying or dividing by a negative number. Let’s walk through a quick example.
We know that 9 is greater than 5. But if we multiply both sides of this inequality by -1, we get -9 > -5, which is not correct. On the number line, multiplying by -1 moves us from the positive side to the negative side, where the order of the numbers is reversed. So, although 9 > 5, it is also true that -9 < -5.
This switch in order explains why the inequality symbol must be flipped whenever we multiply or divide an inequality by a negative number.
Let’s practice with an example.
Example 2: Solving an Inequality When Multiplying or Dividing by a Negative Number
If -14x + 1 ≥ 7x – 5, which of the following cannot be a value of x ?
- 2
- 1/4
- 0
- -1/4
- -2
Solution:
Our first goal is to isolate x:
-14x + 1 ≥ 7x – 5
-21x ≥ -6
Next, we divide by -21 and reverse the direction of the inequality sign.
x ≤ -6/-21
x ≤ 3/7
Let’s use the number line to determine which answer choice is not in the solution set.
All answer choices except x = 2 are in the solution set.
Answer: A
Multiplying or Dividing an Inequality by a Variable — Caution!
We know that whenever we multiply or divide an inequality by a negative number, we must reverse the direction of the inequality sign. There’s another situation that can be just as tricky: multiplying or dividing an inequality by a variable. Let’s check out an example:
If 4ab < 8b, what is the range of possible values for a ?
At first glance, we might want to divide both sides by 4b and conclude that x < 2. But this is not valid, because we don’t know whether b is positive or negative. The solution actually depends on the sign of b, so we need to consider 2 separate cases.
If b = 1, substituting -1 for b into the inequality, we have 4a(1) < 8(1), so a < 2.
However, if b = -1, we have 4a(-1) < 8(-1) → -4a < -8 → a > 2.
The solution set depends on whether b is positive or negative. If the sign of b is unknown, we cannot state a single definitive solution for the possible values of a.
KEY FACT:
We cannot divide an inequality by a variable unless we know the sign of the variable.
Let’s take a look at an example.
Example 3: Multiplying an Inequality by a Variable
Is x > y ?
- x/y > 1
- y > 0
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Solution:
We need to determine whether x > y.
Statement (1) Alone:
x/y > 1
Although we may be tempted to multiply both sides by y to get x >y, we cannot because we don’t know the sign of y! Thus, statement (1) is not sufficient to answer the question. We can eliminate choices A and D.
Statement (2) Alone:
y > 0
Just knowing that y is greater than 0 is not enough information to answer the question. Statement (2) alone is not sufficient. We can eliminate choice B.
Statements (1) and (2) Together:
Using the statements together, we know from statement (2) that y > 0. This allows us to simplify the inequality x/y > 1, from statement (1), by multiplying both sides by y, which gives x > y. Therefore, the 2 statements together are sufficient to answer the question.
Answer: C
Compound Inequalities
Up to this point, we’ve worked with inequalities that use only a single inequality sign, such as x > 7 or 7x < 6.
We also need to understand compound inequalities (sometimes called 3-part inequalities). These link 3 expressions with 2 inequality signs.
For example: -4 < n < 10 means that n is greater than -4 and less than 10.
TTP PRO TIP:
Compound inequalities involve 3 expressions connected by 2 inequality signs.
Let’s now discuss how to simplify compound inequalities.
Simplifying Compound Inequalities
Compound inequalities can be solved using the same methods we use for solving basic inequalities. There are 2 key points to remember when simplifying or manipulating them:
- Any operation you perform on 1 part of a compound inequality must be applied to all parts.
- If you multiply or divide the entire compound inequality by a negative number, you must reverse the direction of both inequality signs.
Let’s look at an example:
-6 > -3n > -30
If we divide the compound inequality by -3, we reverse the direction of the inequality sign and perform the division:
-6 / -3 < -3n / -3 < -30 / -3
2 < n < 10
Notice that when we divided each term by -3, we also flipped the inequality signs.
KEY FACT:
What you do to 1 part of a compound inequality, you do to all parts.
Let’s practice with an example.
Example 5: Compound Inequalities
If -8 < 4x + 2 < 16, how many nonnegative integers could be the value of x?
- 0
- 1
- 2
- 3
- 4
Solution:
First, we must solve the compound inequality -8 < 4x + 2 < 16.
-8 < 4x + 2 < 16
-10 < 4x < 14
-10/4 < x < 14/4
-5/2 < x < 7/2
-2.5 < x < 3.5
The possible integer values of x are -2, -1, 0, 1, 2, and 3. Of these, the nonnegative values are 0, 1, 2, and 3. Thus, there are 4 possible nonnegative integer values of x.
Answer: E
Summary: EA Inequalities Questions
In this article, we learned how to solve inequalities on the Executive Assessment.
An inequality shows a relationship between 2 expressions that are not equal.
Solving a simple inequality follows the same process as solving a linear equation. The difference is that instead of getting a single solution, the result is a range of values on the number line.
The rules for working with inequalities are much like those for linear equations, but there are 2 important exceptions:
- When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.
- If you multiply or divide by a variable, you must know whether that variable is positive or negative before proceeding.
Finally, compound inequalities involve 2 inequality signs and 3 expressions. There are 2 important rules to keep in mind:
- Any operation performed on 1 part of the inequality must be applied to all parts.
- If you multiply or divide any part of a compound inequality by a negative number, you must reverse the direction of both inequality signs.
In this article, we solved a variety of EA inequality Problem Solving and Executive Assessment Data Sufficiency inequalities to highlight the various inequality rules.
Frequently Asked Questions (FAQ)
Are inequalities common on the Executive Assessment?
Although inequalities do appear on the EA, it’s tough to say whether that topic or any quant topic is “common,” just because so few questions from any topic are asked on any given EA exam. Inequalities are just 1 example of Executive Assessment algebra basics that you must master to score well.
What math rules should I memorize for inequalities?
The 2 best rules to memorize are:
- When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.
- If you multiply or divide an inequality by a variable, you must know whether that variable is positive or negative before proceeding.
How are inequalities tested in Data Sufficiency vs Problem Solving?
In Problem Solving, you’re typically asked to solve for the range of possible values of a variable. In Data Sufficiency, the test focuses more on whether the information given is enough to determine the relationship, rather than on finding the exact solution.
Is EA inequality math easier than on the GMAT?
In regard to EA vs GMAT inequalities: generally, yes — the EA tends to test inequalities in more straightforward ways. On the GMAT, inequality questions can be trickier and more layered, often involving multiple variables or advanced reasoning. That said, you still need a thorough understanding of inequalities to correctly answer those questions on the EA.
How much time should I spend practicing inequalities for the EA?
While there is no exact number of hours you need to spend learning inequalities, just make sure you spend enough time to feel comfortable answering any inequality question that comes your way on test day.
What’s Next?
While it’s certainly important to have inequalities mastered for your EA, your Executive Assessment test prep math topics are numerous. If you are wondering how to best prepare for EA quant, check out our article about how to improve your EA quant score.
You can learn practical Executive Assessment quantitative strategies and Executive Assessment math tips by reading our article about quant tips to prepare you for the exam.
