Question:medium

% of students of a class took Statistics and 45% took Mathematics. If each student took Statistics or Mathematics and 40 took both, the total number of students in the class was:

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For two sets $A$ and $B$, $|A\cup B|=|A|+|B|-|A\cap B|$. If “everyone chose at least one,” then $|A\cup B|=N$.
Updated On: Jul 15, 2026
  • 160
  • 180
  • 200
  • 225
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The Correct Option is A

Approach Solution - 1

Step 1: Since every student takes at least one subject, adding the two percentages counts the overlap twice. The combined percentage is \( 80\%+45\%=125\% \), which is 25 percentage points more than the whole class.

Step 2: This extra 25 percent of the class is exactly the group counted twice, the students who take both subjects, given as 40 students.

Step 3: So 25 percent of the total equals 40 students, which means the total is \( \frac{40}{0.25}=160 \).
\[ \boxed{160} \]
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Approach Solution -2

Since every student takes at least one of the two subjects, anyone not counted among the Statistics takers must be taking Mathematics alone. This means the only-Mathematics group is exactly \( 100\%-80\%=20\% \) of the class, and subtracting this from the total Mathematics share of 45 percent gives the overlap: \( 45\%-20\%=25\% \). We can test each option by checking whether 25 percent of it equals the given overlap of 40 students.

  1. 160: 25 percent of 160 is \( 0.25 \times 160=40 \), matching the given overlap exactly.
  2. 180: 25 percent of 180 is \( 0.25 \times 180=45 \), not 40.
  3. 200: 25 percent of 200 is \( 0.25 \times 200=50 \), not 40.
  4. 225: 25 percent of 225 is \( 0.25 \times 225=56.25 \), not 40.

Since students not taking Statistics must be taking only Mathematics, the overlap works out to exactly 25 percent of the class, and only a class of 160 makes that 25 percent equal to the given 40 students.

Therefore, the correct answer is 160.

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