Last year in Country X, 15% of all students who received an undergraduate degree received their degree from a Type...

Understanding the Question

We need to find: What percentage of Type 1 university graduates received STEM degrees?

Given Information

• 15% of all undergrads graduated from Type 1 universities
• 30% of all STEM undergrads graduated from Type 1 universities

What We Need to Determine

We're looking for this specific ratio: \(\frac{\mathrm{STEM\ graduates\ from\ Type\ 1}}{\mathrm{Total\ graduates\ from\ Type\ 1}} \times 100\%\)

Key Insight

Here's the crucial observation: Type 1 universities are overrepresented among STEM graduates. While they account for only 15% of all undergrads, they produce 30% of STEM graduates. This 2:1 ratio tells us something important—Type 1 universities must have a higher concentration of STEM students than the general undergraduate population.

To find our answer, we need to understand how the overall STEM percentage translates to Type 1 universities specifically.

Analyzing Statement 1

Statement 1 tells us: 30% of all undergraduate students received STEM degrees.

Now we can apply our key insight about the 2:1 overrepresentation. Since Type 1 universities produce STEM graduates at twice the rate they produce overall graduates (30% vs 15%), they must have twice the STEM concentration of the general population.

Let's think through this step by step:

• General population: 30% STEM
• Type 1's overrepresentation factor: \(30\% \div 15\% = 2\)
• Therefore, Type 1 universities: \(30\% \times 2 = 60\%\) STEM

This makes intuitive sense—if Type 1 universities are punching above their weight in STEM production, they must have a higher percentage of STEM students than average.

[STOP - Sufficient!] Statement 1 is sufficient. We can definitively answer that 60% of Type 1 graduates received STEM degrees.

This eliminates choices B, C, and E.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: 9,000 students received STEM degrees from Type 1 universities.

This gives us an absolute number, but what we need is a percentage. Without knowing the total number of graduates from Type 1 universities, we cannot determine what portion 9,000 represents.

Consider these possible scenarios:

• If Type 1 universities had 10,000 total graduates: \(9,000 \div 10,000 = 90\%\) STEM
• If Type 1 universities had 15,000 total graduates: \(9,000 \div 15,000 = 60\%\) STEM
• If Type 1 universities had 90,000 total graduates: \(9,000 \div 90,000 = 10\%\) STEM

Each scenario is mathematically consistent with the information given. We simply don't have enough information to determine the total number of Type 1 graduates.

Statement 2 is NOT sufficient—multiple different percentages are possible.

This eliminates choices B and D.

The Answer: A

Statement 1 alone gives us the crucial piece of information (overall STEM percentage) that, combined with the given 2:1 ratio, allows us to calculate the exact percentage. Statement 2 only provides a count without the context we need.

Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."