Study Materials for 2023 CFA®, FRM®, Actuarial, GMAT® and EA® Exams

# Executive Assessment Quantitative Practice Questions

### What is the EA Quantitative Reasoning Questions Exam Structure?

You have 30 minutes to complete 14 questions in this section.

For the first half, the target is to spend 12 minutes allowing a maximum of 15 minutes. You will be spending an average of  2-2.5 minutes on each question. Similar to the first two sections, it is possible to miss up to two questions in this half and still get the 10+ scale score for this section, which is usually the target for most candidates. So if you get stuck on something, don’t spend more valuable time on it at the expense of other questions that you might be able to complete more easily.

Seek out opportunities for logical estimation and alternative tactics. This will allow you to save some time to spend on the harder questions of the second half.

For the second half, you will have 15-18 minutes in total. You will have roughly 2-3 minutes on average for each question. Work through the full half completing “easier” questions first. “Easier” is a relative term, simply answer the questions you are better at first then come back to the “harder” questions in the section.

The quantitative reasoning section of questions consists of data sufficiency and problem-solving questions.

1. Data Sufficiency Questions
Each data sufficiency question is made up of a question and two statements. To answer a question, one should first identify the statement that provides information relevant to the question, and then eliminate all the other possible answers by using math knowledge and other everyday facts.

2. Problem-solving Questions
Each problem-solving question includes a question section and five possible answers to choose from. The questions are designed to assess your use of logic and analytical reasoning to answer quantitative problems.

### What are the Skills and Strategies to Excel in Quantitative Reasoning Questions?

#### Math Skills

Quantitative reasoning questions call for the application of math knowledge to solving problems. Such mathematical skills include:

• Basic arithmetic including fractions, integers, powers and roots, and statistics and probability.
• Algebraic topics such as variables, functions, and solving equations.
• Word problems such as algebraic and geometric principles and blending arithmetic used to solve problems.
• Geometry, particularly geometrical objects such as triangles, circles, quadrilaterals, solids, cylinders, and coordinate geometry.

#### Essential Strategies in Problem Solving Questions

• Always check your onscreen timer. Apply caution while solving questions but don’t waste too much time verifying answers; strive to complete a given section.
• If you find a question difficult or time-consuming, try to eliminate answer choices that might be outrightly wrong and select your best choice from the remaining ones.
• Study each question in depth to ascertain what is being asked. For example, you may need to come up with some equations.
• Solve the questions by writing to limit errors. An erasable tablet will be provided at the test center.
• For the data sufficiency questions, ascertain whether the question requires only one value or a range of values. Moreover, avoid unnecessary assumptions about geometrical figures, as they are not usually drawn to scale.
• Go through the answer choices before answering a question to get the gist of what kind of answer choice structure you are required to present. Moreover, some questions require simple approximation presentations, which may require little mental activity rather than long computations.
3.5  Million
50  Thousand
# 1  Rated

## Division & Factoring

If $$\frac{72}{x}-x = y$$ and $$x$$ is a positive integer less than 10, how many positive integer values are possible for $$y$$?

A) $$9$$

B) $$7$$

C) $$6$$

D) $$2$$

E) $$1$$

To satisfy the conditions of the problem, $$x$$ must be a factor of 72 less than 10, which are 1, 2, 3, 4, 6, 8, and 9.
\begin{align} 1: \frac{72}{1}-1 &= 71\\ 2: \frac{72}{2}-2 &= 34\\ 3: \frac{72}{3}-3 &= 21\\ 4: \frac{72}{4}-4 &= 14\\ 6: \frac{72}{6}-6 &= 6\\ 8: \frac{72}{8}-8 &= 1\\ 9: \frac{72}{9}-9 &= -1\\ \end{align}
Therefore, 6 integer values less than 10 for $$x$$ produce positive integer values for $$y$$.

## Descriptive Statistics

If $$A$$ is the range of the first seven positive multiples of 3, and if $$a$$ is the average of the first seven positive multiples of 3, what is the value of $$A + a$$?

A) 3

B) 6

C) 12

D) 18

E) 24

The first seven positive multiples of 3 are 3, 6, 9, 12, 15, 18, and 21.

The range, $$A$$, can be found by subtracting 3 from 21 as 18.

The average, $$a$$, which can be found efficiently by knowing that the median will be equal to the average in the arithmetic sequence formed by the consecutive multiples of 3, is 12.

Hence, the value of $$A – a = 18 – 12 = 6$$.

## Linear Algebra

During a season of volleyball, a girls’ team won 75% of the first 112 games they played and 25% of the remaining games they played that season. If the team won 60% of their games for the overall season, how many games total did they play?

A) 142

B) 156

C) 160

D) 162

E) 172

If X is the total amount of games the team played, then $$.75(112) + .25(X-112) = .6X$$.

\begin{align*} 84 + .25X – 28 & = .6X \\ 56 & = .35X \\ X &= 160. \end{align*}

## Question 4

If $$b$$ is a constant, how many unique solutions does the equation $$\dfrac{1}{2}x^2-bx+b^2=0$$ have?

A) 0

B) 1

C) 2

D) 3

E) 4

Note that evaluating the discriminant of $$b^2 – 4ac$$ against 0 will be sufficient to determine the number of solutions.

If the discriminant is greater than 0, then there are two solutions for the equation. If it is equal to 0, there is a single solution, and if it is less than 0, there are no real solutions for the equation.

The discriminant of this equation is:
\begin{align*} (-b)^2-4(\dfrac{1}{2})(b^2) &=b^2-2b^2\\ &=-b^2 < 0\\ \end{align*}

Since the discriminant is negative, the equation has no real solutions.

## Functions & Symbols

If [y] denotes the greatest integer less than or equal to y, is [y] = 4?

(1) $$y < 5$$

(2) $$2y + 32 > 40$$

A) Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

B) Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are not sufficient.

It is useful to note that the condition [y] = 4 is equivalent to $$4 < y \leq 5$$

(1) A value of y = 2.5 satisfies this statement, and yields [y] = 2.
A value of y = 4.5 also satisfies this statement, and yields [y] = 4; NOT sufficient.

(2) This statement can be rewritten as y > 4, which allows both by y = 4.5 (yielding [y] = 4) and y = 10.5 (yielding [y] = 10); NOT sufficient.
(Together) The two inequalities yield $$4 < y \leq 5$$, which yields [y] = 4 for any possible value of y; SUFFICIENT.

The correct answer is C; the statements together, but not alone, are sufficient.

## Plane Geometry

A blue rectangular rug and a red rectangular rug each cover the same number of square feet of a floor when they are laid out. If the blue rug is 8 feet wide by 24 feet long and the red rug is 6 feet wide, how much longer is the red rug than the blue rug?

A) 6

B) 8

C) 12

D) 24

E) 32

Find the area of the blue rug by multiplying its length and width: $$24 × 8 = 192$$.

Now, use the area formula to find the length of the red rug as $$192 = 6 × length$$.

192 divided by 6 is 32, and 32 is 8 feet longer than 24.

## 3D Geometry

Tom made an aquarium with a capacity of 20 cubic feet. If Tom were to make a similar aquarium that was twice as long, twice as wide, and twice as high, what would be its volume in cubic feet?

A) 8

B) 100

C) 120

D) 130

E) 160

When every dimension is multiplied by 2, the volume increases by a factor of 2 × 2 × 2 = 8, regardless of the exact dimensions.

Therefore, 20 × 8 = 160 square feet.

## Coordinate Geometry

In the coordinate plane, is point P equidistant from points (2, 4) and (6, 4)?

(1) Point P lies on the line y = 5.

(2) Point P has an x-coordinate of 4.

A) Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

B) Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are not sufficient.

Point P will be equidistant from (2, 4) and (6, 4) if and only if P lies on the perpendicular bisector of the line segment with endpoints (2, 4) and (6, 4).

Therefore, point P will be equidistant from (2,4) and (6,4) if and only if it lies on the vertical line $$x = \frac {(6+2)}{2} = 4$$. Therefore, determine if the x-coordinate of P is 4.

(1) Given that y = 5, then both x = 4 and x $$\neq$$ 4 are possible; NOT sufficient.

(2) Because x = 4, point P must be equidistant from (2,4) and (6,4); SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.

## Rates and Work

Concrete X consists solely of cement and a gravel mixture. If the approximate ratio, by mass, of cement to gravel mixture in Concrete X is 1:7, approximately how many grams of gravel mixture are there in 112 grams of Concrete X?

A) 72

B) 80

C) 98

D) 102

E) 110

The mass ratio of Concrete X is $$\frac{\text{gravel mixture}}{\text{gravel mixture}+\text{cement}} = \frac{7}{1+7} = \frac{7}{8}$$

So, if x is the number of grams of gravel mixture in 112 grams of concrete X, it follows that $$\frac{x}{112} = \frac{7}{8}$$

Solve for x. $$x = \frac{7}{8} * \frac{112}{1} = \frac{7 \times 7 \times 2 \times 2 \times 2 \times 2}{2 \times 2 \times 2} = 7 \times 7 \times 2 = 98$$ grams of gravel in 112 grams of Concrete X.

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