At a public university, the ratio of the number of undergraduate students to the number of… — GRE General Test

At a public university, the ratio of the number of undergraduate students to the number of graduate students at the beginning of an academic year was $4$ to $1$ . By the end of the academic year, the number of undergraduate students had increased by $15\%$ , and the total student population (undergraduate and graduate combined) had increased by $18\%$ . By what percent did the number of graduate students increase?

Answer: 30 %

Answer

30%

Representing the initial populations by their ratio components (

4

parts undergraduate,

1

part graduate,

5

parts total), an overall growth of

18\%

across

5

total parts yields

5 \times 0.18 = 0.90

total parts of growth. The undergraduate population grew by

15\%

, contributing

4 \times 0.15 = 0.60

parts of growth. The remaining

0.90 - 0.60 = 0.30

parts of growth must come from the graduate student component. Since the initial graduate population was

1

part, a growth of

0.30

parts corresponds to a

30\%

increase.

Step-by-Step Solution

Set up initial component values using the ratio

4:1

Undergraduates =

400

, Graduates =

100

, Total =

500

Choosing convenient numbers compatible with the

4:1

ratio simplifies percentage calculations.

Calculate the updated undergraduate count after a

15\%

increase

New Undergraduates =

460

An increase of

15\%

means the new value is

115\%

of the original

400

Calculate the updated total count after an

18\%

increase

New Total =

590

An overall increase of

18\%

means the new total is

118\%

of the original

500

Subtract the new undergraduate count from the new total count to find the new graduate count

New Graduates =

130

The total population is the sum of undergraduate and graduate populations.

Calculate the percent change for the graduate population

30\%

The increase of

30

graduate students over the initial

100

graduate students represents a

30\%

increase.

Key Concept

Weighted percentage change across subgroup components

Estimated Time:2m 0s

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