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GRE Quantitative Reasoning QUESTION #8163
Question 1

A graduating class has 236 students. Among them, 142 enrolled in algebra and 121 enrolled in chemistry. What is the greatest possible number of students who could have taken both algebra and chemistry?

  • $100$
  • $110$
  • $121$✔️
  • $142$
Correct Answer Explanation

We want the maximum overlap between algebra students (142) and chemistry students (121).

The overlap is maximized when every chemistry student also took algebra (since 121 < 142, this is possible).

Maximum overlap $= \min(142, 121) = \mathbf{121}$.

Check: if 121 students took both, then students taking at least one subject $= 142 + 121 - 121 = 142 \leq 236$. ✓

So the greatest possible number is $121$.