In the figure given below, the rectangle represents the 100 families of a colony, and the three circles show the families that keep a dog, a cat and fish as pets. Each number is the number of families in that region.
How many families keep a dog or a cat (or both) but do not keep fish?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 44
The required families lie inside the Dog circle or the Cat circle but outside the Fish circle.
Dog only: 21
Cat only: 16
Dog and cat, no fish: 7
6, 3 and 5 are left out, as they lie inside the Fish circle; 31 lies outside the Dog and Cat circles
Total \(=21+16+7=44\)
Checking the other options
Option (1): 58 — Incorrect. This also counts 6, 5 and 3, which lie inside the Fish circle.
Option (3): 37 — Incorrect. This leaves out the 7 families that keep both a dog and a cat but no fish.
Option (4): 75 — Incorrect. This also counts the 31 families outside all the circles, who keep neither a dog nor a cat.