Last year in Country X, 15% of all students who received an undergraduate degree received their degree from a Type...
GMAT Data Sufficiency : (DS) Questions
Last year in Country X, \(15\%\) of all students who received an undergraduate degree received their degree from a Type 1 university, while \(30\%\) of all students who received an undergraduate degree in a STEM (science, technology, engineering, or mathematics) major received their degree from a Type 1 university. Last year in Country X, what percent of all students who received an undergraduate degree from a Type 1 university received an undergraduate degree in a STEM major?
- Last year in Country X, \(30\%\) of all students who received an undergraduate degree received an undergraduate degree in a STEM major.
- Last year in Country X, a total of \(9,000\) students received a degree in a STEM major from a Type 1 university.
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."