Question:
A researcher found that 70% of people who own a cat also own a dog, but only 20% of dog owners also own a cat. If there are 1,001 dog owners, how many cat owners are there?
A researcher found that 70% of people who own a cat also own a dog, but only 20% of dog owners also own a cat. If there are 1,001 dog owners, how many cat owners are there?
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The "intersection" of two sets is the key link in percentage-based word problems.
Updated On: Jun 12, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
We use the principle of set theory: the number of people who own both is constant regardless of whether you calculate it via dog owners or cat owners.
Step 2: Detailed Explanation:
1. Let \( D \) be the number of dog owners and \( C \) be the number of cat owners.
2. Intersection (Both) = 20% of \( D \).
- Both = \( 0.20 \times 1001 = 200.2 \).
3. We are also told that 70% of cat owners own a dog:
- Both = \( 0.70 \times C \).
4. Equate the two:
- \( 0.70 \times C = 200.2 \).
- \( C = 200.2 / 0.7 = 286 \).
Step 3: Final Answer:
There are 286 cat owners.
We use the principle of set theory: the number of people who own both is constant regardless of whether you calculate it via dog owners or cat owners.
Step 2: Detailed Explanation:
1. Let \( D \) be the number of dog owners and \( C \) be the number of cat owners.
2. Intersection (Both) = 20% of \( D \).
- Both = \( 0.20 \times 1001 = 200.2 \).
3. We are also told that 70% of cat owners own a dog:
- Both = \( 0.70 \times C \).
4. Equate the two:
- \( 0.70 \times C = 200.2 \).
- \( C = 200.2 / 0.7 = 286 \).
Step 3: Final Answer:
There are 286 cat owners.
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