Ratio, Proportion, and Percent Calculations Alıştırma Soruları — GMAT

Soru 1Soru →

Based on the data provided in the table below regarding student enrollment across four university departments in 2025, the percentage of international students in the Business department is greater than the percentage of international students in the Engineering department.

Department	Total Students	International Students
Humanities	400	80
Business	600	150
Science	500	125
Engineering	800	160

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Cevabı ve açıklamayı göster

Cevap: True

Cevap

True

The statement is true. In the Business department, international students account for

\frac{150}{600} = 25\%

of total students. In the Engineering department, international students account for

\frac{160}{800} = 20\%

of total students. Since

25\% > 20\%

, the percentage is indeed greater in Business.

Adım Adım Çözüm

1

Calculate the percentage of international students in the Business department

\frac{150}{600} \times 100\% = 25\%

To find the percentage, divide the number of international students in Business by the total number of students in Business and multiply by 100.

2

Calculate the percentage of international students in the Engineering department

\frac{160}{800} \times 100\% = 20\%

To find the percentage, divide the number of international students in Engineering by the total number of students in Engineering and multiply by 100.

3

Compare the two calculated percentages

25\% > 20\%

Comparing

25\%

(Business) to

20\%

(Engineering) confirms that the proportion is higher in Business.

Anahtar Kavram

Calculating and comparing subgroup proportions and percentages using department-specific total bases

Soru 2Soru →

The table below presents operational metrics for municipal EV charging infrastructure across six urban transit sectors in 2025.

Transit Sector	Total EV Stations	Fast-Charging Stations	Total Energy Delivered (MWh)	Commercial Fleet Usage (MWh)
Sector Alpha	120	36	4,800	1,440
Sector Beta	200	80	7,500	3,000
Sector Gamma	150	45	5,000	1,250
Sector Delta	90	54	3,600	2,160
Sector Epsilon	160	32	6,400	1,600
Sector Zeta	80	48	2,800	1,960

Evaluate the following statement as True or False based on the information provided:

Among all transit sectors where fast-charging stations constitute at least $40\%$ of the total EV stations, the overall proportion of total energy delivered that was consumed by commercial fleets is greater than $50\%$ .

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Cevabı ve açıklamayı göster

Cevap: True

Cevap

True

The qualifying sectors (Beta, Delta, Zeta) have a combined commercial fleet energy consumption of

7,120

MWh out of

13,900

MWh total energy delivered, yielding an overall percentage of

51.22\%

, which exceeds

50\%

.

Adım Adım Çözüm

1

Calculate the fast-charging station percentage for each transit sector to filter qualifying sectors.

Sectors Beta (

40\%

), Delta (

60\%

), and Zeta (

60\%

) qualify with fast-charging proportions

\ge 40\%

.

Filtering rows based on a specified threshold is required before aggregating cross-column data.

2

Sum the total energy delivered and commercial fleet energy usage for the qualifying sectors.

Total energy delivered =

7,500 + 3,600 + 2,800 = 13,900

MWh. Commercial fleet usage =

3,000 + 2,160 + 1,960 = 7,120

MWh.

Calculating weighted overall percentages requires finding the sum of part values over the sum of whole values.

3

Compute the overall commercial fleet energy percentage for the qualifying sectors.

\frac{7,120}{13,900} \approx 51.22\%, which is strictly greater than 50\%.

Demonstrates whether the statement's inequality condition holds true.

Anahtar Kavram

Weighted Aggregated Percentage Calculation from Filtered Table Rows

Soru 3Soru →

The table below details the quarterly revenues for four operating divisions of a logistics firm in 2025:

Division	Q1 Revenue ($)	Q2 Revenue ($)
North	$80,000$	$100,000$
South	$150,000$	$180,000$
East	$120,000$	$144,000$
West	$200,000$	$230,000$

What is the percentage increase in revenue from Q1 to Q2 for the North division?

20\%

25\%

80\%

125\%

12.5\%

Cevabı ve açıklamayı göster

Cevap: $25\%$

Cevap

The percentage increase in revenue for the North division from Q1 to Q2 is

25\%

.

The percentage increase is calculated as

\frac{\text{Q2 Revenue} - \text{Q1 Revenue}}{\text{Q1 Revenue}} \times 100\%

. For the North division,

\frac{100,000 - 80,000}{80,000} = \frac{20,000}{80,000} = 0.25 = 25\%

.

Adım Adım Çözüm

1

Find the absolute change in revenue for the North division from Q1 to Q2.

Change =

\$100,000 - \$80,000 = \$20,000

.

Percentage increase requires comparing the change relative to the initial starting value.

2

Identify the base (initial) value for the percentage calculation.

Base value = Q1 revenue =

\$80,000

.

The base for percentage change calculation is always the initial period value (Q1).

3

Calculate the percentage increase by dividing the change by the base value and multiplying by

100\%

.

Percentage Increase =

\frac{20,000}{80,000} \times 100\% = 0.25 \times 100\% = 25\%

.

To convert a ratio to a percentage, multiply the fractional increase by

100

.

Anahtar Kavram

Percentage Change from Table Data

Tahmini Süre:45s

Soru 4Soru →

The table below displays the vehicle fleet composition across four regional divisions of a logistics corporation.

Division	Electric Vehicles	Gasoline Vehicles	Total Vehicles
North	120	280	400
South	160	240	400
East	90	210	300
West	230	270	500

What percentage of the total fleet across all four divisions consists of electric vehicles?

Cevabı ve açıklamayı göster

Cevap: 37.5

Cevap

The percentage of the total fleet consisting of electric vehicles across all four divisions is

37.5\%

.

To find the overall percentage of electric vehicles, sum the number of electric vehicles across all divisions (

120 + 160 + 90 + 230 = 600

) and divide by the overall total number of vehicles (

400 + 400 + 300 + 500 = 1600

). Dividing

600

by

1600

gives

0.375

, which equals

37.5\%

.

Adım Adım Çözüm

1

Calculate the total number of electric vehicles across all divisions.

120 + 160 + 90 + 230 = 600

electric vehicles.

Summing the electric vehicle column values gives the total count of electric vehicles.

2

Calculate the total vehicle count across all divisions.

400 + 400 + 300 + 500 = 1600

total vehicles.

Summing the total vehicle column values provides the aggregate denominator.

3

Compute the required percentage.

\frac{600}{1600} \times 100\% = 37.5\%

.

Dividing total electric vehicles by total vehicles yields the aggregate proportion.

Anahtar Kavram

Ratio, Proportion, and Percent Calculations

Tahmini Süre:1m 0s

Soru 5Soru →

The table below displays quarterly logistics metrics for five regional distribution hubs of a global shipping enterprise in 2025:

Hub	Total Units Shipped	Air Freight Share (%)	Q1 Avg Shipping Cost per Unit ($)	Q4 Avg Shipping Cost per Unit ($)
North	50,000	30%	120	168
South	60,000	40%	200	260
East	40,000	25%	150	213
West	75,000	20%	160	192
Central	30,000	35%	80	108

For the hub that experienced the greatest percentage increase in average shipping cost per unit from Q1 to Q4, what is the ratio of its air freight unit volume to the non-air freight unit volume of the hub with the highest total overall expenditure in Q4?

5 : 18

1 : 6

5 : 12

10 : 9

2 : 3

Cevabı ve açıklamayı göster

Cevap: $5 : 18$

Cevap

The ratio of the air freight unit volume of the hub with the greatest percentage cost increase (East) to the non-air freight unit volume of the hub with the highest Q4 expenditure (South) is 5 : 18.

East has the greatest percentage cost increase (

42.0\%

), yielding

10,000

air freight units. South has the highest total Q4 expenditure (

\$15,600,000

), with a non-air freight unit volume of

36,000

. The simplified ratio of these two quantities is

10,000 : 36,000 = 5 : 18

.

Adım Adım Çözüm

1

Calculate the percentage increase in average shipping cost per unit from Q1 to Q4 for each hub.

North:

\frac{168 - 120}{120} = 40.0\%

South:

\frac{260 - 200}{200} = 30.0\%

East:

\frac{213 - 150}{150} = 42.0\%

West:

\frac{192 - 160}{160} = 20.0\%

Central:

\frac{108 - 80}{80} = 35.0\%

Identify which hub achieved the greatest percentage increase in per-unit cost.

2

Identify the target hub and calculate its air freight unit volume.

The hub with the highest percentage increase is East (42.0%). Its air freight unit volume is

25\%

of

40,000 = 10,000

units.

Formulate the numerator for the final ratio.

3

Calculate total Q4 expenditure for each hub to find the hub with the highest overall expenditure.

North:

50,000 \times \$168 = \$8,400,000

South:

60,000 \times \$260 = \$15,600,000

East:

40,000 \times \$213 = \$8,520,000

West:

75,000 \times \$192 = \$14,400,000

Central:

30,000 \times \$108 = \$3,240,000

The hub with the highest total Q4 expenditure is South ($15,600,000).

4

Calculate the non-air freight unit volume for South.

South non-air freight share

= 100\% - 40\% = 60\%

. Non-air freight volume

= 60\%

of

60,000 = 36,000

units.

Formulate the denominator for the final ratio.

5

Compute and simplify the final ratio.

\frac{10,000}{36,000} = \frac{10}{36} = \frac{5}{18}

or

5 : 18

.

Express the relationship in simplest integer ratio form.

Anahtar Kavram

Multi-Step Tabular Ratio and Percentage Analysis

Soru 6Soru →

The table below details capital allocation, exit valuations, active portfolio companies, and successful exits across five high-technology sectors for a venture capital firm in 2026.

Sector	Capital Invested ($M)	Realized Exit Valuation ($M)	Active Portfolio Companies	Successful Exits
AI Infrastructure	450	1,350	18	6
Clean Energy	320	560	16	4
Enterprise SaaS	600	1,500	25	10
Advanced Robotics	250	375	10	3
BioHealth & Genomics	400	880	12	5

Evaluate the following statement based on the data provided:

The overall return multiple (total realized exit valuation divided by total capital invested across all five sectors combined) is less than the percentage return on investment (net gain divided by capital invested) achieved by the BioHealth & Genomics sector.

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Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. The overall return multiple across all five sectors (

2.3094\times

, representing

230.94\%

) is greater than the percentage ROI for BioHealth & Genomics (

120\%

).

The evaluated statement is False. Calculating the total sum of capital invested across all sectors yields

\$2,020\text{M}

, and the total sum of realized exit valuations yields

\$4,665\text{M}

. The overall return ratio is

\frac{4665}{2020} \approx 2.3094

(or

230.94\%

). In contrast, the percentage ROI for BioHealth & Genomics is calculated on its net gain:

\frac{880 - 400}{400} = 1.20

(or

120\%

). Comparing the two values reveals that

2.3094 > 1.2000

, contradicting the statement's claim that the overall multiple is less.

Adım Adım Çözüm

1

Calculate the total capital invested across all five sectors.

Total Capital Invested =

450 + 320 + 600 + 250 + 400 = \$2,020\text{ million}

.

Aggregating the column provides the denominator for the combined return multiple.

2

Calculate the total realized exit valuation across all five sectors.

Total Exit Valuation =

1,350 + 560 + 1,500 + 375 + 880 = \$4,665\text{ million}

.

Aggregating the column provides the numerator for the combined return multiple.

3

Compute the overall return multiple across all sectors.

Overall Multiple =

\frac{\$4,665\text{M}}{\$2,020\text{M}} \approx 2.3094

(or

230.94\%

of capital invested).

Determines the benchmark value stated in the prompt.

4

Calculate the percentage ROI for the BioHealth & Genomics sector.

BioHealth Net Gain =

\$880\text{M} - \$400\text{M} = \$480\text{M}

. BioHealth ROI =

\frac{\$480\text{M}}{\$400\text{M}} \times 100\% = 120\%

.

Percentage ROI measures net profit relative to initial capital invested.

5

Compare the overall return multiple to the BioHealth percentage ROI.

2.3094 > 1.2000

(or

230.94\% > 120\%

). The statement claims the overall multiple is less than the BioHealth ROI, which is incorrect.

Direct comparison evaluates the truth value of the target statement.

Anahtar Kavram

Distinguishing Total Return Multiples from Net Percentage ROI and Aggregating Tabular Data

Tahmini Süre:2m 30s

Soru 7Soru →

The table below presents operational metrics and financial allocations for six municipal water treatment facilities in 2025.

Facility	Total Water Processed (Million Gallons)	Recycled Water (Million Gallons)	Distribution Loss Rate (%)	Annual Operating Budget ($ Millions)
Alton	450	90	8%	18.0
Belton	600	150	12%	21.0
Colton	350	70	6%	14.0
Dalton	700	210	15%	22.4
Easton	500	130	10%	17.5
Fulton	400	80	5%	16.0

For the facility with the lowest operating budget per million gallons of total water processed, what percentage of its total processed water was recycled?

Cevabı ve açıklamayı göster

Cevap: 30

Cevap

30%

Evaluating the unit budget per million gallons processed across all facilities reveals that Dalton has the lowest operating rate at

22.4\text{M} / 700\text{ MG} = \$0.0320\text{M / MG}

. Computing the percentage of total processed water that was recycled for Dalton gives

(210 / 700) \times 100\% = 30\%

.

Adım Adım Çözüm

1

Calculate operating budget per million gallons processed for each facility to determine unit cost.

Alton = 0.0400; Belton = 0.0350; Colton = 0.0400; Dalton = 0.0320; Easton = 0.0350; Fulton = 0.0400 ($M per MG).

To identify which facility operates with the lowest financial cost per unit of water processed.

2

Identify the minimum unit cost value among all six facilities.

Dalton has the lowest operating budget per million gallons ($0.0320M per MG).

Dalton satisfies the condition of having the lowest operating budget per million gallons processed.

3

Divide Dalton's recycled water volume by its total processed water volume and express as a percentage.

(210 / 700) * 100% = 30%.

To find the specific proportion of recycled water relative to total processed water at the identified facility.

Anahtar Kavram

Unit Rate Comparison and Percentage Calculation from Tabular Data

Soru 8Soru →

The table below presents energy and cost metrics for six commercial data center facilities operated by a cloud computing provider in fiscal year 2025.

Facility	IT Load Capacity (MW)	Renewable Energy Used (GWh)	Total Energy Consumption (GWh)	Operational Cost ($M)
Alpha	40	180	240	36.0
Beta	65	312	390	54.6
Gamma	25	100	160	22.4
Delta	80	360	480	72.0
Epsilon	50	225	300	42.0
Zeta	90	486	540	75.6

Statement: If the operational cost of facility Beta increases by 15% in 2026 while its IT load capacity remains unchanged, its 2026 operational cost per megawatt (MW) of IT load capacity will exceed the 2025 operational cost per megawatt of facility Alpha by more than 8%.

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Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

The statement is False because facility Beta's 2026 operational cost per MW (

0.966M/MW) exceeds facility Alpha's 2025 operational cost per MW (

0.900M/MW) by approximately 7.33%, which is less than 8%.

The correct evaluation is False. Facility Alpha's unit operational cost is

0.900M per MW (

36.0M / 40 MW). Facility Beta's unit cost in 2025 is

0.840M per MW (

54.6M / 65 MW). A 15% increase brings Beta's 2026 unit cost to

0.966M per MW. Comparing Beta's 2026 rate (

0.966M) to Alpha's 2025 rate (

0.900M) gives a relative increase of (

0.966 -

0.900) /

0.900 = 7.33%, which does not exceed 8%.

Adım Adım Çözüm

1

Calculate facility Alpha's 2025 operational cost per MW of IT load capacity.

Facility Alpha cost per MW =

36.0M / 40 MW =

0.900M per MW.

Establishes the base value against which the 2026 rate will be compared.

2

Calculate facility Beta's 2025 operational cost per MW and its updated 2026 rate after a 15% increase.

Facility Beta 2025 rate =

54.6M / 65 MW =

0.840M per MW. Facility Beta 2026 rate =

0.840M × 1.15 =

0.966M per MW.

Applies the 15% growth rate to Beta's cost per unit capacity.

3

Compute the percentage change (excess) of facility Beta's 2026 rate relative to facility Alpha's 2025 rate.

Percentage excess = (

0.966M -

0.900M) / $0.900M = 0.066 / 0.900 = 7.33%.

Evaluates whether the percentage difference exceeds the 8% threshold requested in the statement.

Anahtar Kavram

Unit Rate Calculations and Percentage Change Base Selection

Soru 9Soru →

The table below presents operational patient data across five regional health centers for fiscal year 2025.

Regional Health Center	Total Inpatient Admissions	Emergency Department Visits	Outpatient Telehealth Consultations	30-Day Inpatient Readmissions
Central Metro	12,000	45,000	18,000	1,440
North Ridge	8,000	25,000	15,000	880
Eastside	15,000	60,000	20,000	1,500
Valley Pines	6,000	18,000	12,000	540
West Coast	10,000	32,000	14,000	1,100

Across all five regional health centers combined, what percentage of total inpatient admissions resulted in a 30-day inpatient readmission?

2.4%

3.0%

10.6%

10.7%

12.0%

Cevabı ve açıklamayı göster

Cevap: 10.7%

Cevap

10.7%

To calculate the aggregate percentage across all five regional health centers, sum the total number of readmissions (

1,440 + 880 + 1,500 + 540 + 1,100 = 5,460

) and divide by the sum of total inpatient admissions (

12,000 + 8,000 + 15,000 + 6,000 + 10,000 = 51,000

). Dividing

5,460

by

51,000

yields approximately

0.10706

, or

10.7\%

.

Adım Adım Çözüm

1

Calculate the total number of 30-day inpatient readmissions across all five regional health centers.

1,440 + 880 + 1,500 + 540 + 1,100 = 5,460

To find aggregate percentage, the combined numerator must be determined.

2

Calculate the total number of inpatient admissions across all five regional health centers.

12,000 + 8,000 + 15,000 + 6,000 + 10,000 = 51,000

The question specifically asks for readmissions as a percentage of total inpatient admissions, establishing the base denominator.

3

Divide total readmissions by total inpatient admissions and convert to a percentage.

\frac{5,460}{51,000} \times 100\% \approx 10.70588\% \approx 10.7\%

Determines the combined weighted percentage of readmissions.

Anahtar Kavram

Weighted aggregate percentage calculation from tabular data

Tahmini Süre:1m 30s

Soru 10Soru →

The table below presents subscriber numbers and annual operating revenue data for five regional divisions of a telecommunications provider in fiscal year 2025.

Region	Total Broadband Subscribers (thousands)	Fiber-Optic Subscribers (thousands)	Total Operating Revenue ($ millions)
North	250	150	45.0
South	400	200	64.0
East	180	90	27.0
West	320	224	57.6
Central	500	350	80.0

Across the two regional divisions with the highest total operating revenue combined, fiber-optic subscribers represent what percentage of total broadband subscribers? Express your answer to the nearest tenth of a percent.

Cevabı ve açıklamayı göster

Cevap: 61.1

Cevap

61.1%

To find the proportion of fiber-optic subscribers across the top two revenue-generating divisions, first rank the divisions by Total Operating Revenue: Central (

80.0M) and South (

64.0M) are the highest. Combine their subscriber counts to find the appropriate base: Central has 500 thousand total broadband subscribers and South has 400 thousand, giving a total base of

500 + 400 = 900

thousand. Next, combine their fiber-optic subscribers: Central has 350 thousand and South has 200 thousand, giving

350 + 200 = 550

thousand fiber-optic subscribers. The combined percentage is

\frac{550}{900} \times 100\% \approx 61.111\%

, which rounds to

61.1\%

.

Adım Adım Çözüm

1

Identify the top two divisions by operating revenue

Central (

80.0M) and South (

64.0M)

The question specifically restricts the calculation to the two divisions with the highest operating revenue.

2

Sum total broadband subscribers for Central and South

500 + 400 = 900 thousand subscribers

This establishes the correct aggregate base value for the percentage calculation.

3

Sum fiber-optic subscribers for Central and South

350 + 200 = 550 thousand subscribers

This gives the total combined numerator value for the fiber-optic subgroup.

4

Calculate percentage and round to the nearest tenth

(550 / 900) * 100% = 61.111...% -> 61.1%

Dividing the target subgroup total by the base total yields the requested proportion.

Anahtar Kavram

Ratio, Proportion, and Percent Calculations across Filtered Aggregate Groups

Tahmini Süre:1m 30s

Ratio, Proportion, and Percent Calculations

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Adım Adım Çözüm

Anahtar Kavram

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