Question

10. Last February had 28 days and each night in that month Maria had a dream. Some of her dreams involved dogs, some involved cats and some involved no animals at all. You are given that 16 involved dogs, 15 involved cats and 4 involved no animals at all. How many of Maria's dreams involved BOTH dogs and cats? (A) 3 (B) 5 (C) 7 (D) 9 (E) 11​

Answer 1

I believe the answer would be C. 7

Explanation:

Let's use the principle of inclusion-exclusion to find the number of dreams that involved both dogs and cats.

Total Dreams=Dreams with Dogs+Dreams with Cats−Dreams with Both+Dreams with No Animals

Given: Dreams with Dogs=16, Dreams with Cats=15, Dreams with No Animals=4

Substitute these values into the formula:

Total Dreams(y)=16+15−Dreams with Both(x)+4

Now, solve for the number of dreams(y) that involved both dogs and cats, Substituting the dreams with both using x:

X=16+15+4−(y)

Since the total number of dreams is the number of nights in February (28), we can substitute this value:

X=35−28

Dreams with Both=7

Therefore, the number of dreams that involved both dogs and cats is 77.

I hope this helps!