In a certain biology class, there are 6 more graduate students than

Question

In a certain biology class, there are 6 more graduate students than undergraduate students. Exactly 30 percent of the graduate students and exactly 37.5 percent of the undergraduate students are foreign students. What is the smallest possible number of foreign students in the class?

A. 12
B. 15
C. 18
D. 21
E. 24

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Official Answer

C

A. 12
B. 15
C. 18
D. 21
E. 24

egmat · Answer

Since we're counting students, the number of foreign students must be a  whole number . This means the percentages must work out evenly.

Setting Up: 
Let U = number of undergraduates
Then G = U +  6  (graduates)

The Hidden Constraints: 
 • 30% of G must be a whole number → 30% = 3/10, so G must be divisible by 10 
 • 37.5% of U must be a whole number → 37.5% = 3/8, so U must be divisible by 8

Finding the Smallest Valid Numbers: 
We need U divisible by  8 : so U = 8, 16, 24, 32...
And G = U + 6 must be divisible by  10 .

Let's test:
• U =  8  → G = 14  (not divisible by 10 ✗) 
• U =  16  → G = 22  (not divisible by 10 ✗) 
• U =  24  → G = 30  (divisible by 10 ✓)

Calculating Foreign Students: 
• Foreign graduates = 30% ×  30  =  9 
• Foreign undergraduates = 37.5% ×  24  =  9 
• Total = 9 + 9 =  18

Answer: C (18)

General Principle:  When percentages must yield whole numbers, convert them to fractions and find what the total must be divisible by. Then find the smallest value satisfying ALL constraints.

kevincan · Answer

Beautifully explained !

Edskore · Answer

This is a great problem that disguises number properties inside a word problem. The key concept being tested is integer constraints on percentages — the GMAT loves checking whether you recognize that certain percentages force specific divisibility requirements.
Step 1: Define variables
Let g = number of graduate students, u = number of undergraduate students.
We know g = u + 6.
Step 2: Apply the percentage constraints

30% of graduate students are foreign → 0.30 × g must be an integer → g must be a multiple of 10 (since 30% = 3/10).
37.5% of undergraduate students are foreign → 0.375 × u must be an integer → u must be a multiple of 8 (since 37.5% = 3/8).

This is the step most people skip too quickly. They jump straight to plugging numbers without first pinning down the divisibility rules.
Step 3: Find the smallest values satisfying both constraints
We need the smallest g (multiple of 10) and u (multiple of 8) where g = u + 6.
Try u = 8 → g = 14 (not a multiple of 10) ✗
Try u = 16 → g = 22 (not a multiple of 10) ✗
Try u = 24 → g = 30 (multiple of 10) ✓
Step 4: Calculate the foreign students

Foreign grads = 30% × 30 = 9
Foreign undergrads = 37.5% × 24 = 9
Total foreign students = 9 + 9 = 18

Answer: C
Common trap: Students often pick A (12) by trying u = 8 and g = 10 without checking that g = u + 6 must hold simultaneously. Always verify ALL constraints before calculating.
Takeaway: Whenever a GMAT problem gives you percentages that must yield whole numbers of people, immediately convert those percentages to fractions and identify the divisibility requirement — it dramatically narrows your search.

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