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

# Executive Assessment Data Sufficiency Questions

### What is the Structure of EA Data Sufficiency Questions?

There are two sections in EA quantitative reasoning questions: problem-solving and data sufficiency. Data sufficiency questions measure your ability to analyze a quantitative problem, determine the relevant data, and determine if there is enough data to solve it.

Data sufficiency questions include a question and two statements. The first step in answering the question is to identify the statement that provides relevant information. Next, use math knowledge and other everyday facts to eliminate all other possible answers.

### Tips for Data Sufficiency Questions

• The quantitative takes 30 minutes to complete and includes 14 questions. Therefore, you do have, on average, two minutes to answer each question.
• There are 6 to 7 data sufficiency questions in every quantitative section.
• Determine whether the problem allows only a single value or a range of values. Note that the primary objective is to determine whether there is enough data to solve the problem.
• Avoid unnecessary assumptions about geometrical figures, as they are not necessarily drawn to scale.
• Remember to always ask, “Am I making progress toward a solution?” If not, immediately move to the next question because otherwise, you are wasting time, which is a very important factor in this test. Do, however, allow a calm reread, recalculation, or a tactical reset before you guess and move on.
4.5  Million
50  Thousand
# 1  Rated

## Division & Factoring

Is the ratio of x to y greater than 2?

(1) $$x+2=y$$

(2) $$x=8$$

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.

(1) If $$x+2 =y$$, then $$\frac{x}{y}+\frac{2}{y}=1$$ or $$\frac{x}{y}=1-\frac{2}{y}.$$ More information is required to define the inequality; NOT sufficient.

(2) That $$x=8$$ provides no information about $$y$$; NOT sufficient.

(Together) $$x+2 =y$$ and $$x=8$$ hence $$y=8+2=10$$. Therefore, $$\frac{x}{y}=\frac{8}{10} < 2$$ producing a definitive answer of always no; SUFFICIENT.

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

## Number Properties

Is integer $$n$$ even?

(1) $$n^0$$ is an odd integer.

(2) $$x^n+2$$ is an even integer.

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.

(1) Since any value raised to the 0 power is 1, this provides no information about the value of $$n$$; NOT sufficient.

(2) This only determines that $$x$$ is an even integer but provides no information about the value of $$n$$; NOT sufficient.

(Together) There are still no limitations on the value of $$n$$; NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

## Percentages (Data Sufficiency)

If x is 75 percent of y, what is the value of x?

(1) $$y > 300$$

(2) $$y – x = 45$$

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.

(1) To find the value of x requires a single value for x or y. This statement only provides a minimum value, and so the question cannot be answered; NOT sufficient.

(2) Substitute the given value of y in terms of x, which is $$y = \frac {4}{3}x$$, to produce the equation $$\frac {4}{3}x – x = 45$$ which can be solved for the single variable of x as equal to 105; SUFFICIENT.

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

## Exponents & Radicals (Data Sufficiency)

Is $$–4 \le x \le 4$$?

(1) $$x^2 + y^2 = 16$$

(2) $$x^2 + y \le 16$$

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.

(1) That $$x^2 + y^2 = 16$$ indicates that both x and y must be between – 4 and 4 inclusive as all squares must be positive values; SUFFICIENT.

(2) Subtract y from each side of the inequality to produce $$x^2 \le 16 – y$$. Because there is no limit on the value of y, there is no limit on the value of x, and so the answer cannot be answered definitively; NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.

## 3D Geometry (Data Sufficiency)

Three-quarters of a cylindrical tank is filled with water. What is the area of the tank’s surface that is in contact with the water?

(1) The diameter of the tank is a third of the height of the tank.

(2) The ratio of the base area to that of the curved surface is 1 to 12.

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.

Area of the curved surface = $$2\pi rh$$ where $$r$$ and $$h$$ are the radius of the base and the height of the cylinder, respectively, and the area of the base touching water is $$\pi r^2$$.

(1) $$\frac{1}{3}h=d=2r$$ hence $$r=\frac{1}{6}h$$ or $$h=6r$$, but no values are provided for either variable; NOT sufficient.

(2) The ratio = $$\frac{\pi r^2}{2\pi rh}=\frac{r}{2h}=\frac{1}{12}$$, and $$r$$ in terms of $$h$$ is $$r=\frac{h}{6}$$; NOT SUFFICIENT.

(Together) Both statements produce the same equation $$r=\frac{h}{6}$$ for two unknowns; NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

## Inequalities

Does a single butterscotch candy cost less than a single licorice candy?

(1) The total cost of 5 butterscotch candies and 4 licorice candies is less than the total cost of 3 butterscotch candies and 7 licorice candies.

(2) The total cost of 4 butterscotch candies and 3 licorice candies is more than total cost of 3 butterscotch candies and 2 licorice candies.

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.

Let the cost of a single butterscotch candy be $$b$$ and the cost of a single licorice candy be $$l$$. Determine whether $$b < l$$.

(1) Articulate algebraically as $$5b + 4l < 3b + 7l$$

Subtract $$3b$$ and $$4l$$ from each side to find that $$2b < 3l$$ or $$b$$ < <sup>3</sup>&frasl;<sub>2</sub> $$l$$. Therefore, $$b$$ may or may not be less than $$l$$; NOT sufficient</p>

(2) Articulate algebraically as $$4b + 3l < 3b + 2l$$

Subtract $$3b$$ and $$2l$$ from each side to find that $$b < l$$ and therefore, the answer to the question is the cost of a single butterscotch candy less than the cost of a single licorice candy is always no; SUFFICIENT.

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

## Plane Geometry

What is the sum of the degrees of the interior angles of polygon Q?

(1) Polygon Q has 8 sides.

(2) One of the interior angles of polygon Q is $$135^{\circ}$$.

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.

(1) The sum of the degrees of the interior angles for any polygon is $$(n – 2) \times 180$$, where n represents the number of sides of the polygon.

Therefore, the sum of the degrees of polygon Q is $$(8 – 2) \times 180 = 1080$$; SUFFICIENT.

(2) No information is provided for the sum of the degrees nor the number of vertices of polygon Q; NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.

## Descriptive Statistics

In a class of 20 students, the sum of the first 19 scores of a test is 1197. What is the average score for the test for all 20 students?

(1) The 20th student’s score is equal to the average score.

(2) The 20th student’s score was 30% higher than the average score.

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.

(1) Let $$x$$ be the 20th score, so that the average score of the 20 students is equal to $$x$$ as $$\frac{1197+x}{20}=x$$.

Multiply by 20 to find, $$20x=1197+x$$ and subtract $$x$$ to find that $$19x=1197$$.

Divide by 19 to find that $$x=63.$$; SUFFICIENT.

(2) Recognize that a similar equation can be derived from this statement that can be solved for $$x$$; SUFFICIENT.

The correct answer is D; each statement alone is sufficient.

## Coordinate Geometry

Points A and B are connected to a common point D by two line segments in the coordinate plane that intersect at $$60^{\circ}$$. How far is point A from point B?

(1) Point A lies in the first quadrant.

(2) The points lie on the arc of a circle.

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.

(1) The location of the two points is neither given nor the lengths of the segments; NOT sufficient.

(2) The points lie on a circle, but their location is not provided; NOT sufficient.

(Together) Two points on a circle are connected by a chord whose central angle is $$60^{\circ}$$, but the radius of the circle is not given; NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

## Rates, Work, and Combined Time

Cars enter a parking garage at a certain rate. At the same time, cars leave the parking garage at a different rate. At what rate, in cars per minute, is the number of cars in the garage changing?

(1) Cars enter the garage at a rate of 13.5 cars per 4.5 minutes.

(2) Cars leave the garage at a rate of 5 cars per minute.

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.

(1) While this rate can be converted to $$\frac {13.5}{4.5} = 3$$ cars/minute entering the garage, it says nothing about the rate at which cars leave; NOT sufficient.

(2) This statement says nothing about the rate at which cars enter the garage; NOT sufficient.

(Together) With the rates at which cars both enter and leave the garage, the target question can be answered; SUFFICIENT.

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