Let's solve this problem step by step.

Step 1: Define the given data

• 10% of the cats preferred Moggiemeat.
• 20% of the cats preferred Fuss-a-Puss.
• 40% of the cats preferred Yummy Paws.
• 6 cats did not have a preference.
• 27 cats did not eat any of the three foods.

Step 2: Calculate the total percentage of cats that showed a preference for the foods

The percentage of cats that showed a preference for any of the foods: $10\% + 20\% + 40\% = 70\%$

Step 3: Let the total number of cats be $x$

According to the problem, 70% of the cats prefer one of the three foods: $0.7x \text{ cats prefer one of the foods.}$

The remaining 30% of the cats did not have a preference or refused to eat the foods: $0.3x = 6 \text{ (no preference)} + 27 \text{ (refused all foods)}$

Step 4: Solve for $x$

$0.3x = 6 + 27$ $0.3x = 33$ $x = \frac{33}{0.3} = 110$

So, the total number of cats in the survey is 110.

Final Answer

The correct answer is e) 110.

Would you like more details or have any questions? Here are some related questions:

1. What percentage of the total cats had no preference for any of the foods?
2. How many cats preferred Moggiemeat, Fuss-a-Puss, and Yummy Paws respectively?
3. If the survey included 200 cats, how many would you expect to have no preference?
4. How would the percentages change if 10 more cats refused all foods?
5. What is the probability of randomly selecting a cat that prefers Yummy Paws?

Tip: When dealing with percentage problems, always start by assigning a variable to the total amount, and express everything else in terms of that variable.