Executive Assessment Math Problems with Solutions

If you are currently studying for the Executive Assessment (EA) and are in the thick of your prep, you already know the importance of practicing EA math problems. To help with your practice, we’re presenting you with a representative selection of EA math problems with solutions. Of course, practicing the questions here is just a start. If you need more practice after completing what we offer in this article, please check out the Target Test Prep Online Executive Assessment Course.

Executive Assessment Math Problems with Solutions

Here are the topics we’ll cover:

Before we jump into examples of EA math questions, let’s discuss some key basics of EA Quant.

The Structure of the Executive Assessment

The EA has three sections, and they are always presented in this order:

  1. Integrated Reasoning (IR)
  2. Verbal Reasoning
  3. Quantitative Reasoning

Unlike the GMAT Focus, the EA does not allow you to choose the section order. You have 30 minutes to complete the questions in each EA section.

The IR section contains 12 questions, subdivided into two 6-question panels. The first panel contains questions of mixed difficulty levels. After you submit all answers in your first IR panel, the second panel will base its difficulty level on your performance on the first panel. Difficult questions, answered correctly, will enhance your score more than correctly answered easier questions. So, it is to your benefit to do as well as you can on the questions in the first panel.

The second section, Verbal Reasoning, presents you with 14 questions. You will again have two panels, and each panel will consist of 7 questions. Here’s an interesting twist: the difficulty level of the first Verbal panel depends in part on how well you performed on the IR section! And the difficulty of the second Verbal panel will reflect your performance on the first Verbal panel.

The Quantitative Reasoning section is similarly structured as the Verbal Reasoning section. The 14 math questions appear in two panels, with difficulty levels based on your IR performance and/or your performance on the first panel of the Quantitative Reasoning section.

You may think that the EA structure is a bit convoluted, but this “panel-adaptive” difficulty level allows for the EA to assess your skills quite accurately, even though the exam length is short and the number of questions is minimal.

KEY FACT:

The Executive Assessment is “panel-adaptive,” allowing for a short exam with relatively few questions to be highly accurate.

The Topics Tested in the Quant Section of the EA

The good news regarding the topics in the EA Quant section is that they are similar to those you studied in high school. The bad news is that it may have been quite a few years since high school! You might be rusty at material you learned long ago. But, as you jump into your EA math prep or take practice tests, I’m sure many concepts and techniques will come back to you.

However, as you may have already discovered, not all of the math questions you see on the Executive Assessment are the same types of questions you saw in high school. The EA, especially the Data Sufficiency questions, will test your ability to think much more analytically. So, you will train new math “muscles” as you learn EA Quant.

TTP PRO TIP:

The topics tested on the EA are similar to those you saw in high school, but the question types might not be.

Before we consider the types of math questions on the EA, let’s take a look at the topics covered.

An Overview of the Executive Assessment Quant Topics

  • Basic Arithmetic:PEMDAS; estimation; decimals; fractions; factorials
  • Linear Equations: linear equations (one variable and two variables); using the combination method and the substitution method to solve a linear system; isolating a particular variable in an equation.
  • Quadratic Equations: factoring and FOILing; quadratic identities; the zero-product property; solving fractional equations
  • Exponents and Roots: adding, subtracting, multiplying, and dividing exponential expressions; rationalizing the denominator; square roots and other roots; negative exponents; fractional exponents; solving exponential equations
  • Number Properties: even/odd and positive/negative integers; prime numbers; LCM and GCF; remainder theory; divisibility; evenly spaced sets; units digits patterns
  • Inequalities: equations versus inequalities; arithmetic operations on inequalities; multiplying an inequality by a negative number; compound inequalities
  • Absolute Value: definition of absolute value; solving absolute value equations; when two absolute value expressions are equal
  • General Word Problems: age, money, consecutive integers, and mixtures; business word problems: salary, profit/loss, simple interest, and compound interest; linear and exponential growth
  • Rates: basic rates; average rates; converging/diverging rates; catch-up rates; catch-up and pass rates; round trip rates
  • Work: basic work; combined work and opposing work questions
  • Unit Conversions: basic unit conversions; conversions with squared or cubed units
  • Ratios and Proportions: two-part and three-part ratios; the ratio multiplier; setting up and solving proportion problems
  • Percents: basic percents; percent of; percent less than or greater than; percent change
  • Overlapping Sets: the set matrix; calculations using the set matrix; Venn diagrams
  • Statistics: mean, median, mode; weighted average; evenly spaced sets; range and standard deviation
  • Combinations and Permutations: combination and permutation formulas; fundamental counting principle; restricted and non-restricted combinations; indistinguishable permutations; circular permutations; creating codes
  • Probability: probability rules; mutually exclusive events; addition rule; independent events; multiplication rule
  • Coordinate Geometry: coordinate axes; slope and y-intercept; parallel and perpendicular lines; midpoint and distance formulas; circles; graphing inequalities
  • Functions and Sequences; function notation; domain and range; compound functions; function word problems; graphing functions; sequences: arithmetic and geometric

KEY FACT:

There are 19 major topics on the EA Quant section, and each topic has many subtopics.

The list of topics and subtopics might appear overwhelming, but it’s good to know what to expect from the get-go. To quote Sun Tzu: “Know the enemy and know yourself, and in a hundred battles you will never be in peril.”

Now, let’s discuss the EA Quant question types.

The EA Quant Question Types

In the Executive Assessment Quant section, you will encounter 2 main types of Quant questions: Problem-Solving (PS) and Data Sufficiency (DS) problems. Of the 14 questions in the Quant section of the EA, roughly 8 will be PS questions and 6 will be DS questions.

KEY FACT:

Of the 14 questions in EA Quant, 8 are Problem-Solving questions and 6 are Data Sufficiency questions.

Let’s take a close look at Problem-Solving questions.

EA Problem-Solving Questions

You are already familiar with EA Problem-Solving questions. This multiple-choice question type presents 5 answer choices: A, B, C, D, and E. There is only one correct answer for each question.

Any concept can be tested in a PS question, including all 19 topics we listed previously. Let’s look at 6 EA Problem Solving practice questions, each representing one of the major topics.

Problem-Solving Example 1: Quadratic Equations

What is the value of 97^2 – 3^2?

  • 9,391
  • 9,400
  • 9,409
  • 9,500
  • 10,000

Solution:

If you recognize that this question is about the difference of squares, you can solve it in less than 30 seconds.

Recall the fact that, for any numbers a and b, the difference of squares can be expressed as a^2 – b^2 = (a – b)(a + b). We can apply this equation to the expression in the question stem, with a = 97 and b = 3. Thus, we can re-express  97^2 – 3^2 as follows:

97^2 – 3^2 = (97 – 3)(97 + 3) = (94)(100) = 9,400

Note that if you didn’t know the shortcut provided by the difference of squares identity, you could have instead solved this question by doing the time-consuming arithmetic: 97^2 = 9409 and then subtracting 3^2 = 9, to obtain 9,400. But, instead, by recognizing the difference of squares concept, we have avoided the risk of making an arithmetic mistake, and we’ve saved a lot of time, which can be used later in the Quant section.

Answer: B

Problem-Solving Example 2: Number Properties

What is the units digit of 3^15?

  • 9
  • 7
  • 5
  • 3
  • 1

Solution:

When we raise the base 3 to successive positive integer powers, we can determine the pattern of the units (ones) digit. Let’s calculate the first few powers of 3 to discern the pattern.

3^1 = 3 units digit is ;

3^2 = 9 units digit is 9

3^3 = 27 units digit is 7

3^4 = 81 units digit is 1

3^5 = 243 units digit is 3

So, we see that the units digits of powers of 3 have a repeating pattern of 4 numbers: 3-9-7-1. Thus, every 4th exponent has the same units digit. For example, we see that 3^4, 3^8, 3^12, … etc., will all have the same units digit of 1.

The most straightforward way of determining the units digit of 3^15 is to find an exponent that is a multiple of 4 and close to 15. The pattern shows us that 3^16 must have a units digit of 1. So, using the pattern 3-9-7-1, we see that 3^15 must have a units digit of 7.

Answer: B

Problem-Solving Example 3: Exponents

If 27x + 2 * 96 = 816, then x is equal to which of the following?

  • 2
  • 3/2
  • 1
  • 1/2
  • 0

Solution:

The first step is to get like bases. In this case, the current bases, 27, 9, and 81, can all be expressed as powers of 3. So, we will use the facts that 27 = 3^3, 9 = 3^2, and 81 = 3^4, to rewrite the equation:

27x + 2 * 96 = 816

(33)x + 2 * ( 32)6 = ( 34)6

33x + 6 * 312 = 324

Now that all terms have the same base, we can combine them:

33x + 6 + 12 = 324

33x + 18 = 324

We can now use the fact that when the bases are the same, we can equate the exponents:

3x + 18 = 24

3x = 6

x = 2

Answer: A

Problem-Solving Example 4: General Word Problems

Jethro bought only apples and pears at the market, spending a total of $16.00. He bought twice as many pears as apples. Pears cost $1.50 each, and apples cost $1.00 each. How many pieces of fruit did he buy?

  • 6
  • 9
  • 12
  • 15
  • 16

Solution:

First, let’s define our two variables:

a = the number of apples Jethro bought

p = the number of pears Jethro bought

Next, we write two equations based on the information presented in the problem.

He spent a total of $16.00, and each apple cost $1.00 and each pear cost $1.50, so we have:

16 = 1a + 1.5p

a = 16 – 1.5p   (equation 1)

Since he bought twice as many pears as apples, we have:

p = 2a         (equation 2)

Next, from equation 1, we can substitute 16 – 1.5p for a in equation 2, and then solve for p:

p = 2(16 – 1.5p)

p = 32 – 3p

4p = 32

p = 8

Now, let’s use equation 2 to solve for a:

p = 2a

8 = 2a

4 = a

Thus, Jethro bought 8 + 4 = 12 pieces of fruit.

Answer: C

Problem-Solving Example 5: Rates

Sanjay walks from home to school at a rate of 4 mph and rides his bike home from school, using the same route, at 15 mph. For the round trip, what is his average speed?

  • 7/2
  • 90/19
  • 100/19
  • 120/19
  • 10

Solution:

Since we have an average rate question we can use the following formula:

average rate = total distance / total time

At first glance, it appears that we do not have enough information to answer the question. But remember that we can use any distance and its associated time to calculate the average rate. For this problem, then, let’s choose a convenient number that is divisible by both 4 and 15 (just to make the arithmetic easier), so let’s let the distance each way be 60 miles.

So, the time going to school is 60/4 = 15, and the time going home from school is 60/15 = 4.

Now we can determine the average rate:

average rate = total distance / total time

average rate = (60 + 60) / (15 + 4)

average rate = 120 / 19

Answer: D

Problem-Solving Example 6: Percents

If r is 300 percent of s, and s is 500 percent of t, then t is what percent of r, rounded to the nearest whole percent?

  • 5
  • 7
  • 12
  • 60
  • 110

Solution:

First, we can note that 300% of a number is equivalent to 3 times that number, and 500% of a number is equivalent to 5 times that number. Next, with these facts in mind, we can create two equations:

r = 3s (equation 1)

s = 5t (equation 2)

We substitute 5t for s in equation 1:

r = 3(5t)

r = 15t  (equation 3)

Now, to determine what percent t is of r, we divide these two quantities and multiply the result by 100%:

t / r ✕ 100%

Finally, we can simplify this expression if we use equation 3, plugging in 15t for r:

t / r ✕ 100% = t/15t ✕ 100% = 1/15 ✕ 100% = 100/15% = 6.67%, which rounds to 7%.

Thus, t is approximately 7% of r.

Answer: B

Problem-Solving Example 7: Combinations and Permutations

A museum has 12 different artifacts in the storage room. The curator must choose 4 of them for a display. In how many possible ways can he select the 4 items?

  • 48
  • 45
  • 99
  • 450
  • 495

Solution:

First, note that the order of selection is of no importance. Therefore, this is a combination problem. Recall the formula for a combination choosing r objects out of n objects is nCr = n! / r!(n – r)!.

Thus, the number of ways to choose the 4 artifacts out of the 12 available artifacts is:

12C4 = 12! / 4!(12 – 4)! = 12! / 4!(8)! = 12 x 11 x 10 x 9 / 4 x 3 x 2 x 1 = 495

Answer: E

EA Data Sufficiency Questions

The Executive Assessment will present you with 6 Data Sufficiency (DS) questions on the two panels of the Quantitative Reasoning section. These 6 questions represent nearly half of the questions in the Quant section, so it is critical that you learn the ins and outs of DS questions!

Data Sufficiency (DS) questions are quite different from Problem-Solving questions. In a PS question, you must come up with a precise number (or variable) answer, but in a Data Sufficiency question, you must decide whether you have sufficient information to determine a definitive answer.

A DS question usually provides information in a problem stem, a question, and 2 statements. Your job is to decide if one statement, either statement, or both statements provide enough information to answer the given question. If this seems a bit confusing, don’t worry. With practice, you can learn the logic underlying DS questions, and soon you’ll be a pro!

KEY FACT:

When solving Data Sufficiency questions, you must decide whether you have enough information to determine an answer.

Let’s look at the DS answer choices.

The Data Sufficiency Answer Choices

Data sufficiency answer choices are the same for every DS question! During your EA preparation, it will serve you well to memorize the DS answer choices. Doing so is as important as memorizing math formulas or math shortcuts.

Here are the DS answer choices:

Answer A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Answer B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Answer C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Answer D: EACH statement ALONE is sufficient to answer the question asked.

Answer E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

TTP PRO TIP:

Memorize the DS answer choices.

Next, let’s discuss the first type of DS question: the value question.

The Value Data Sufficiency Question

We already know that in Data Sufficiency questions, we need to determine whether we have enough information to answer a particular question. In a value question, we need to determine whether we have enough information to generate a single numerical answer.

Let’s look at a few example “value” question prompts:

  • What is the value of a + b?
  • What is the thousandth digit of x?
  • How many students are in Ms Q’s class?
  • What is the average of x and y?
  • For how many days did Clarice rent the car?

TTP PRO TIP:

In value Data Sufficiency questions, our job is to see if we have enough information to determine a single numerical value for the question asked.

Let’s now practice with some examples.

Value DS Example 1: Quadratic Equations

What is the value of m?

1) m > 0

2) m2 = 24m

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct Answer
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • EACH statement ALONE is sufficient.
  • Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

Statement (1) Alone:

Can we determine a unique value for n, using only statement (1)?

Statement (1) tells us that m is greater than 0. Thus, m could be any of an infinite number of numbers. For example, m could equal 3, 9/10, or 1,008,003.

Because statement (1) does not allow us to determine a definitive value for m, we say that statement (1) is insufficient. We can eliminate answer choices A and D.

Statement (2) Alone:

We must solve the quadratic equation m2 = 24m. It might be tempting to divide both sides of the given equation by m. But recall that we cannot divide both sides of an equation by a variable unless we are sure that the variable can’t be equal to 0. In statement (2), we are told nothing about whether m is equal to 0. So, we have to do some other algebra to solve for m:

m2 = 24m

m2 – 24m = 0

m(m – 24) = 0

We see that there are two solutions to the equation: m = 0 or m = 24. Thus, we cannot determine a unique value of m. Therefore, statement (2) alone is not sufficient to answer the question, “What is the value of m?” So, we can eliminate answer choice B.

Both Statements Together:

From the algebra above, we can see that statement (2) tells us that m = 0 or m = 24. Statement (1), meanwhile, tells us that m > 0. Therefore, m cannot equal 0, meaning m must equal 24. So the two statements together allow us to say that there is only one value for m: 24. Therefore, both statements, used together, give us sufficient information to answer the question “What is the value of m?”

Answer: C

Value DS Example 2: Absolute Value

If |3y – 2| = 1, then what is the value of y?

1) y is a positive number

2) y2 < y

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct Answer
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • EACH statement ALONE is sufficient.
  • Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

Before we consider the two statements, we can solve the absolute value equation. We solve it for two cases: when (3y – 2) is positive and when (3y – 2) is negative, as follows:

Case 1: (3y – 2) is positive

3y – 2 = 1

3y = 3

y = 1

Case 2: (3y – 2) is negative

-(3y – 2) = 1

-3y + 2 = 1

-3y = -1

y = 1/3

The absolute value equation has two solutions: y = 1 and y = 1/3.

Statement (1) Alone:

Statement (1) says that y is a positive number. Both possible values of y are positive, so statement (1) by itself is not sufficient to determine a unique value for y. We can eliminate answer choices A and D.

Statement (2) Alone:

We know that the only way that y2 can be less than y is if y is a positive proper fraction — that is, if y is between 0 and 1.

If you aren’t familiar with the rule stated above, consider the following strategy:

  1. If y is a negative number, then y2 will always be positive, and thus y2 will always be greater than y. This is in conflict with statement (2), which states that y2 < y.
  2. If y is a positive number greater than 1, then y2 will always be greater than y. For example, if y = 3, then y2 = 9, so y < y2.  This is also in conflict with statement (2), so y cannot be a positive number greater than 1.
  3. If y is a positive proper fraction, when a positive proper fraction is squared, this squared value is less than the value of the original fraction. Thus, we see that y2 < y is true only if y is a positive proper fraction.

From the question stem, we determined that the two possible values of y are y = 1 and y = 1/3. Statement (2) tells us that y must be a positive proper fraction, and only one possible value of y meets this criterion: y = 1/3. Therefore, statement (2) by itself is sufficient to answer the question.

Answer: B

Next, let’s discuss yes/no Data Sufficiency questions.

The Yes/No Data Sufficiency Question

The yes/no DS question is nearly identical to its “value” counterpart. But our goal is not to find a singular numerical value from the given statements. Instead, we must determine whether we can definitively answer “yes” or “no” to the question posed. If we come up with an answer of “sometimes yes and sometimes no,” then the statement is not sufficient.

TTP PRO TIP:

To determine sufficiency in a yes/no DS question, we must answer a question with a definitive yes or no answer.

Here are a few examples of yes/no DS question prompts:

  • Is a > b?
  • Is the integer p a prime number?
  • Is x between 2 and 5?
  • Is the mode greater than the median?

Let’s practice answering some Yes/No Data Sufficiency questions.

Yes/No DS Example 1- Inequalities

Is  p > 17 – q?

1) p < 9

2) q < 8

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct Answer
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • EACH statement ALONE is sufficient.
  • Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

Question Stem Analysis:

First, let’s rewrite the inequality in the question stem by putting the variables on the same side of the equation. By adding q to both sides of the inequality, the question becomes: Is p + q > 17?

Statement (1) Alone:

We know only that p < 9. So, without any information about the value of q, statement (1) is not sufficient. Eliminate answer choices A and D.

Statement (2) Alone:

We know only that q < 8.  Without any information about the value of p, statement (2) is not sufficient. Eliminate choice B.

Both Statements Together:

From statement (1), we know that p is less than 9, and from statement (2) we know that q is less than 8. Combining this information, we see that the sum of p and q must be less than the sum of 9 and 8, which is 17:

p + q < 17

As a result, we can definitely say that the answer to the question “Is p + q > 17?” is no. The sum p + q  must be less than 17, not greater than 17. Therefore, statements (1) and (2) together are sufficient to answer the yes/no question.

Answer: C

Yes/No DS Example 2: Coordinate Geometry

Is (3, 7) on line m?

1) Line m has a y-intercept of -3.

2) Line m has a positive slope.

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Correct Answer
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • EACH statement ALONE is sufficient.
  • Statements (1) and (2) TOGETHER are NOT sufficient.

Solution:

Question Stem Analysis:

To answer the question, we need to know more about line m.

Statement (1) Alone:

We know that the y-intercept of line m is -3, so line m passes through (0, -3). However, we don’t have enough information to determine if it passes through the point (3, 7), Statement (1) is not sufficient. We can eliminate answer choices A and C.

Statement (2) Alone:

Knowing only that the slope of line m is positive does not give us enough information to answer the question. There are many lines with positive slopes. We can eliminate answer choice B.

Both Statements Together:

The knowledge that both that the y-intercept of line m is -3 and that its slope is positive is not enough to tell us whether the line passes through (3, 7).

For example, the equation y = x – 3 represents a line with a y-intercept equal to -3 and a positive slope equal to 1. Yet this line does not pass through the point (3, 7).

In contrast, the equation y = 3.5x – 3 represents a line that has a y-intercept equal to -3 and a positive slope equal to 3.5, and it does pass through the point (3, 7).

Even with both statements together, we cannot definitely answer the question: “Is (3,7) on line m?” Therefore, both statements together are not sufficient to answer the question.

Answer: E

Summary

Executive Assessment Quant covers 19 major math topics from a variety of topics, from arithmetic to algebra to statistics.

The Quantitative Reasoning section consists of 14 questions, including 8 Problem-Solving questions and 6 Data Sufficiency questions.

  • Problem-Solving (PS) questions are traditional multiple-choice questions with 5 answer choices.
  • Data Sufficiency (DS) questions are questions that require the student to use math and logic to analyze two statements, to determine whether either, both, or neither are sufficient to answer a particular mathematical question.

What’s Next?

The 2 keys to success on EA Quant are knowledge of the 19 topics that are tested and familiarity with the question types. In this article, we have provided you with 11 example questions covering both Problem-Solving and Data Sufficiency questions.

Because you’ve probably never encountered DS questions, you might feel that you need more practice with them. If so, you can read our article focused on Data Sufficiency questions and how to answer them.

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