Question

In a school, 70 play only hockey, 100 play only football, 30 play both the games. 150 do not play anything at all. What is the percentage (rounded to two decimals) of hockey players to total students in the school?

• A. 46.6%
• B. 20%
• C. 28.57%
• D. 66.6%

Hint:

Remember to add the "both" category when calculating the total for one specific game.

Answer 1

The Correct Option is C

Step 1: List the disjoint groups.
Only hockey = 70, only football = 100, both games = 30, neither = 150.
Step 2: Find total hockey players.
Anyone who plays hockey is either hockey-only or plays both, so hockey players $= 70 + 30 = 100$.
Step 3: Add up all students.
Total $= 70 + 100 + 30 + 150 = 350$.
Step 4: Set up the percentage.
Required percentage $= \dfrac{\text{hockey players}}{\text{total students}} \times 100 = \dfrac{100}{350} \times 100$.
Step 5: Simplify the fraction.
$\dfrac{100}{350} = \dfrac{2}{7}$, so the percentage $= \dfrac{200}{7}$.
Step 6: Compute the value.
$\dfrac{200}{7} \approx 28.57\%$.
\[ \boxed{28.57\%} \]