Question

In a survey, 70% of cat owners also own a dog, while only 20% of dog owners also own a cat. If there are 1001 dog owners, how many cat owners are there?

• A. 453
• B. 254
• C. 771
• D. 286

Hint:

For ownership-survey problems, calculate the overlap from one group and equate it to the overlap calculated from the other group.

Answer 1

The Correct Option is D

Concept: The number of people who own both a cat and a dog is the same regardless of whether we count them from the dog-owner group or the cat-owner group. This principle allows us to form an equation.

Step 1: Find the number of people who own both a dog and a cat. Dog owners: \[ 1001 \] 20% of dog owners also own a cat. Therefore, \[ \text{Both}=\frac{20}{100}\times1001 \] \[ =200.2 \]

Step 2: Let total cat owners be \(x\). 70% of cat owners also own a dog. Hence, \[ \frac{70}{100}x=200.2 \] \[ 0.7x=200.2 \] \[ x=\frac{200.2}{0.7} \] \[ x=286 \]

Step 3: Verify. 70% of 286 \[ =200.2 \] which matches the common group calculated from dog owners. Hence calculation is correct. \[ \boxed{x=286} \] Therefore, \[ \boxed{\text{Answer = (D)}} \]