Data Sufficiency with Visual and Tabular Contexts Practice Questions — GMAT

Question 1Question →

The table below displays the number of employees and the average salary per employee across three departments at Company Z:

Department	Number of Employees	Average Salary ($)
Marketing	20	60,000
Engineering	$E$	80,000
Sales	30	50,000

What was the overall average salary per employee across all three departments combined?

(1) The total number of employees across all three departments combined is 100.
(2) The total annual payroll for the Engineering department is $4,000,000.

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

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.

Show answer & explanation

Answer: EACH statement ALONE is sufficient.

Answer

EACH statement ALONE is sufficient.

The question target requires finding the weighted average salary across all departments, which reduces to finding the value of the unknown employee count

E

. Statement (1) yields

20 + E + 30 = 100

, so

E = 50

. Statement (2) yields

E \times 80,000 = 4,000,000

, so

E = 50

. Since each statement independently determines

E

, each statement alone is sufficient.

Step-by-Step Solution

1

Rephrase the question stem target

Overall average salary =

\frac{20(60,000) + E(80,000) + 30(50,000)}{20 + E + 30} = \frac{2,700,000 + 80,000E}{50 + E}

. Finding the value of

E

is sufficient to answer the question.

The overall average salary is a weighted average that depends solely on the single unknown parameter

E

.

2

Evaluate Statement (1) independently

Total employees =

20 + E + 30 = 100 \implies E = 50

. Since

E

is uniquely determined, the overall average salary can be calculated.

Statement (1) provides a direct linear equation in

E

.

3

Evaluate Statement (2) independently

Engineering total payroll =

E \times 80,000 = 4,000,000 \implies E = 50

. Since

E

is uniquely determined, the overall average salary can be calculated.

Statement (2) gives the total department cost, which divided by the known average salary gives

E

directly.

4

Conclude sufficiency classification

Each statement alone gives

E = 50

, making each statement individually sufficient.

Both Statement (1) and Statement (2) yield a unique value for

E

independently.

Key Concept

Weighted average determination from tabular data using Data Sufficiency logic

Estimated Time:1m 0s

Question 2Question →

A regional logistics firm operates four distribution centers: Facility Alpha, Facility Beta, Facility Gamma, and Facility Delta. The table below displays the total tonnage of cargo processed and the average processing cost per ton (in dollars) at each facility during the last quarter:

Distribution Center	Total Tonnage Processed (tons)	Average Cost per Ton ($)
Facility Alpha	2,400	50
Facility Beta	1,600	40
Facility Gamma	$T$	80
Facility Delta	3,000	$C$

Is the overall average processing cost per ton across all four distribution centers combined less than $60?

(1) Facility Gamma processed 2,000 tons of cargo ( $T = 2,000$ ).
(2) Facility Delta's average cost per ton was $55 ($ C = 55$).

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

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.

Show answer & explanation

Answer: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answer

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

The correct answer is the option stating that both statements together are sufficient, but neither alone is sufficient. By setting up the total cost and total tonnage expressions from the table, the question 'Is the overall average cost less than

60?' simplifies to the inequality 'Is

T + 150C < 11,800

?'. Neither statement alone supplies both variables (

T

and

C

), but together they specify

T = 2,000

and

C = 55

, giving

2,000 + 8,250 = 10,250 < 11,800$, which answers the question with a definitive 'Yes'.

Step-by-Step Solution

1

Set up the algebraic expression for the overall combined average processing cost.

Total Tonnage =

2,400 + 1,600 + T + 3,000 = 7,000 + T

.
Total Cost (

) =

(2,400 \times 50) + (1,600 \times 40) + (T \times 80) + (3,000 \times C) = 120,000 + 64,000 + 80T + 3,000C = 184,000 + 80T + 3,000C$.

Weighted average requires dividing total dollar expenditure across all facilities by total tonnage processed.

2

Rephrase the target question inequality.

Is

\frac{184,000 + 80T + 3,000C}{7,000 + T} < 60

?
Multiply by

(7,000 + T)

:

184,000 + 80T + 3,000C < 60(7,000 + T)

184,000 + 80T + 3,000C < 420,000 + 60T

20T + 3,000C < 236,000

Divide by 20:
Is

T + 150C < 11,800

?

Simplifying the target question establishes a direct numerical threshold to test against both statements.

3

Evaluate Statement (1) alone.

Given

T = 2,000

, the target inequality becomes: Is

2,000 + 150C < 11,800 \implies 150C < 9,800 \implies C < 65.33

?
Since

C

is unknown, if

C = 50

, the answer is Yes (

9,500 < 11,800

). If

C = 70

, the answer is No (

12,500 \not< 11,800

).

Statement (1) leaves

C

undetermined, allowing both 'Yes' and 'No' outcomes.

4

Evaluate Statement (2) alone.

Given

C = 55

, the target inequality becomes: Is

T + 150(55) < 11,800 \implies T + 8,250 < 11,800 \implies T < 3,550

?
Since

T

is unknown, if

T = 2,000

, the answer is Yes (

10,250 < 11,800

). If

T = 4,000

, the answer is No (

12,250 \not< 11,800

).

Statement (2) leaves

T

undetermined, allowing both 'Yes' and 'No' outcomes.

5

Evaluate Statements (1) and (2) together.

Combining

T = 2,000

and

C = 55

into the rephrased inequality:

T + 150C = 2,000 + 150(55) = 2,000 + 8,250 = 10,250

.
Since

10,250 < 11,800

, we obtain a definitive 'Yes'.

Both variables are uniquely determined, resolving the target inequality definitively.

Key Concept

Weighted Average Calculation and Data Sufficiency Inequality Rephrasing

Estimated Time:2m 0s

Question 3Question →

A renewable energy research laboratory tested four experimental photovoltaic panel coatings (Coating Alpha, Coating Beta, Coating Gamma, and Coating Delta) across three sunlight intensity levels (Low, Medium, and High). The table below displays the measured power output, in watts per square meter ( $\text{W/m}^2$ ), for each coating under each sunlight intensity level:

Coating	Low Intensity	Medium Intensity	High Intensity
Coating Alpha	80	180	280
Coating Beta	90	195	310
Coating Gamma	75	170	$x$
Coating Delta	$y$	200	320

What is the average (arithmetic mean) power output of Coating Gamma across all three sunlight intensity levels?

(1) Under High Intensity, the power output of Coating Gamma is 10% greater than the power output of Coating Alpha under High Intensity.

(2) The average (arithmetic mean) power output of Coating Delta across the three intensity levels is equal to the average (arithmetic mean) power output of Coating Beta across the three intensity levels.

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

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.

Show answer & explanation

Answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Answer

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

Rephrasing the question target shows that finding the average power output of Coating Gamma requires finding the unknown value

x

. Statement (1) directly gives a percentage relationship between

x

and Coating Alpha's high-intensity output (

280 \text{ W/m}^2

), allowing us to calculate

x = 308

and thus the exact mean. Statement (2) allows us to solve for

y

(Coating Delta's low-intensity output), but provides no information about

x

. Therefore, Statement (1) alone is sufficient, while Statement (2) alone is not.

Step-by-Step Solution

1

Rephrase the question stem target

The average power output of Coating Gamma is

\frac{75 + 170 + x}{3} = \frac{245 + x}{3}

. To find this average, we only need to determine the value of

x

.

Simplifying the question target clarifies that finding

x

is both necessary and sufficient.

2

Evaluate Statement (1)

Statement (1) states that under High Intensity, Coating Gamma (

x

) is 10% greater than Coating Alpha (280). Thus,

x = 280 \times 1.10 = 308 \text{ W/m}^2

. We can compute the average as

\frac{245 + 308}{3} = 184.33 \text{ W/m}^2

.

Since a single unique numerical value for

x

is found, Statement (1) ALONE is sufficient.

3

Evaluate Statement (2)

Statement (2) gives the mean of Coating Delta as equal to the mean of Coating Beta. Mean of Coating Beta =

\frac{90 + 195 + 310}{3} = \frac{595}{3}

. Setting

\frac{y + 200 + 320}{3} = \frac{595}{3}

yields

y = 75 \text{ W/m}^2

.

Finding

y

gives information about Coating Delta, but provides no information regarding

x

for Coating Gamma. Thus, Statement (2) ALONE is not sufficient.

Key Concept

Target Rephrasing and Independent Statement Evaluation in Tabular Data Sufficiency

Estimated Time:2m 0s

Question 4Question →

An investment portfolio consists of three funds: Fund Alpha, Fund Beta, and Fund Gamma. The table below presents the capital committed (in millions of dollars) and the annual yield percentage for each fund during the past fiscal year:

Fund	Capital Committed ($ millions)	Annual Yield (%)
Fund Alpha	40	8%
Fund Beta	60	12%
Fund Gamma	$c$	$y\%$

What was the overall annual yield percentage for the combined portfolio of all three funds?

(1) The capital committed to Fund Gamma, $c$ , was equal to the total capital committed to Fund Alpha and Fund Beta combined.
(2) The annual yield percentage for Fund Gamma, $y\%$ , was equal to the weighted average annual yield percentage of Fund Alpha and Fund Beta combined.

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

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.

Show answer & explanation

Answer: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Answer

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

The option stating that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient is correct. Fund Alpha and Fund Beta combined have a weighted average yield of

\frac{40(8\%) + 60(12\%)}{100} = 10.4\%

. Statement (2) tells us that Fund Gamma's yield is also

10.4\%

. Combining any two groups with identical average yields results in an overall average yield equal to

10.4\%

, regardless of the amount of capital

c

in Fund Gamma. Statement (1) provides only the capital amount

c = 100

, leaving the yield

y

unknown and thus insufficient.

Step-by-Step Solution

1

Formulate the algebraic expression for the overall portfolio yield.

Overall Portfolio Yield =

\frac{40(8\%) + 60(12\%) + c(y\%)}{40 + 60 + c} = \frac{3.2 + 7.2 + \frac{cy}{100}}{100 + c} = \frac{10.4 + \frac{cy}{100}}{100 + c}

The total annual return is the sum of returns from each fund, divided by total capital committed.

2

Calculate the combined weighted average yield of Fund Alpha and Fund Beta.

Sub-portfolio yield =

\frac{40(8) + 60(12)}{40 + 60} = \frac{320 + 720}{100} = 10.4\%

Determining the performance of the known portion of the portfolio simplifies statement evaluation.

3

Evaluate Statement (1) independently:

c = 40 + 60 = 100

.

Overall Yield =

\frac{10.4 + y}{200} \times 100\% = \frac{10.4 + y}{2}\%

. Since

y

is unknown, this value is not unique.

Without knowing Fund Gamma's yield rate

y\%

, the capital amount alone does not provide a definitive overall yield.

4

Evaluate Statement (2) independently:

y\% = 10.4\%

.

Overall Yield =

\frac{100(10.4\%) + c(10.4\%)}{100 + c} = \frac{10.4\%(100 + c)}{100 + c} = 10.4\%

.

When a new component is added to a group with a value equal to the group's current average, the overall average remains unchanged regardless of the size (

c

) of the new component.

Key Concept

Weighted Average Invariance in Data Sufficiency

Data Sufficiency with Visual and Tabular Contexts

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes