How many kids are in the class?

Fourteen of the kids in the class are girls. Eight of the kids wear blue shirts. Two of the kids are neither girls nor wear a blue shirt. If five of the kids are girls who wear blue shirts, how many kids are in the class?

Question:

Fourteen of the kids in the class are girls. Eight of the kids wear blue shirts. Two of the kids are neither girls nor wear a blue shirt. If five of the kids are girls who wear blue shirts, how many kids are in the class?

Answer:

The total number of kids in the class is 19.

Explanation

(A Venn Diagram is shown at the end of the explanation)

Prepare to unravel the mystery of class sizes and student attributes in this thought-provoking puzzle. At first glance, the problem seems complex, but with careful analysis, we will discover the correct solution.

Step 1: Identifying Key Information

  • Girls in the class: 14
  • Kids who wear blue shirts: 8
  • Kids who are neither girls nor wear blue shirts: 2
  • Girls who wear blue shirts: 5

Step 2: Finding the Total Kids in the Class To determine the total number of kids in the class, we must consider all categories: Total kids in the class = Total girls + Kids who wear blue shirts but are not girls + Kids who are neither girls nor wear blue shirts

Step 3: Evaluating the Girls Who Wear Blue Shirts The puzzle explicitly states that five of the kids are girls who wear blue shirts. Total girls who wear blue shirts = 5

Step 4: Identifying Kids Who Wear Blue Shirts but are Not Girls To calculate this number, we subtract the girls who wear blue shirts from the total kids who wear blue shirts. Kids who wear blue shirts but are not girls = Total kids wearing blue shirts – Girls who wear blue shirts Kids who wear blue shirts but are not girls = 8 – 5 = 3

Step 5: Considering Kids Who are Neither Girls nor Wear Blue Shirts The puzzle provides this information directly: two kids are neither girls nor wear blue shirts. Total kids who are neither girls nor wear blue shirts = 2

Step 6: Calculating the Total Kids in the Class Total kids in the class = Total girls + Kids who wear blue shirts but are not girls + Kids who are neither girls nor wear blue shirts Total kids in the class = 14 (girls) + 3 (kids who wear blue shirts but are not girls) + 2 (kids who are neither girls nor wear blue shirts) = 19. This is as shown in the Venn Diagram below:

Fourteen of the kids in the class are girls. Eight of the kids wear blue shirts. Two of the kids are neither girls nor wear a blue shirt. If five of the kids are girls who wear blue shirts, how many kids are in the class?

And there you have it! The correct answer to the puzzle is that there are 19 kids in the class. Your sharp analytical skills have triumphed once again. Happy puzzling!

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