Question:medium

In an examination, 42% of the students passed in at least two subjects out of the three subjects P, Q and R. 36% of the students passed in subjects Q and R. 10% of the students passed in all the three subjects. 38% of the students passed subject P. How many students passed in only subject P?

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Split 'at least two' into exactly-two and all-three, and use the same trick with 'Q and R' to isolate the P-only region.
Updated On: Jul 20, 2026
  • 32%
  • 30%
  • 28%
  • 24%
  • 22%
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The Correct Option is

Solution and Explanation

Instead of pure algebra, plug in real numbers and check them against every given condition. We know the all-three group is 10%, and the exactly-two total is $42-10=32\%$. Since $Q \cap R = 36\%$ includes the all-three group, the "Q and R only" (not P) group is $36-10=26\%$, leaving $32-26=6\%$ split between "P and Q only" and "P and R only" in any combination, say $3\%$ and $3\%$.
Now build the picture: only P $= a$, P&Q only $=3$, P&R only $=3$, all three $=10$, Q&R only $=26$. Since P total is 38%, $a + 3 + 3 + 10 = 38$, so $a = 22$.
Check: Q∩R $=26+10=36$ matches the given data, and at-least-two $=3+3+26+10=42$ also matches. Every condition checks out with only P $=22\%$.
So 22% of the students passed only subject P.
Note: the on-file answer key marks this as 24% (option d), but this fully verified construction, which satisfies every given percentage exactly, gives 22%, matching option (e).
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