Question

Abdul, Mala and Chetan went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds Abdul saw, two were yellow. Of the birds Mala saw, three were yellow. Of the birds Chetan saw, four were yellow. How many yellow birds were seen in all? How many non-yellow birds were seen in all?

• A. 7 yellow birds and 3 non yellow birds
• B. 5 yellow birds and 2 non yellow birds
• C. 4 yellow birds and 2 non yellow birds
• D. 3 yellow birds and 2 non yellow birds

Hint:

There are only 7 distinct birds in total (3 unique, 3 shared by pairs, 1 seen by all); use Chetan's all-yellow set to pin down the rest.

Answer 1

The Correct Option is B

Instead of naming every bird with a letter, we can reason about this puzzle using a simple table of which birds each person saw, working from the person with the strictest clue first.

First, count how many distinct birds exist. Three birds are seen by exactly one person, three more are seen by exactly two people, one is seen by all three, so the total number of distinct birds is 3 + 3 + 1 = 7. Each person's own sightings add up to 4 birds, since a person sees their own unique bird, the two birds they share with the other two people, and the one bird everyone shares, which is 1 + 1 + 1 + 1 = 4.

1. Chetan's clue is the strongest: he saw 4 birds and all 4 were yellow. This means every bird Chetan saw is yellow, with no exceptions, so we know for certain that Chetan's unique bird, the bird he shares with Abdul, the bird he shares with Mala, and the bird all three share, are all yellow. That is already 4 yellow birds confirmed.
2. Abdul's clue narrows things further: Abdul saw 4 birds and only 2 were yellow. Two of Abdul's birds are already known to be yellow from Chetan's list, namely the bird shared between Abdul and Chetan, and the bird shared by all three. Since Abdul's count stops at 2 yellow birds, his other two birds, his own unique bird and the bird he shares only with Mala, must both be non-yellow.
3. Mala's clue finishes the puzzle: Mala saw 4 birds and 3 were yellow. Two of her birds are already known, the bird she shares with Chetan (yellow, from Chetan's list) and the bird all three share (yellow). The bird she shares with Abdul was just found to be non-yellow. That is 2 yellow and 1 non-yellow so far among her 4 birds, so to reach her total of 3 yellow birds, her own unique bird must be yellow.

Putting the seven distinct birds together: Chetan's unique bird (yellow), Mala's unique bird (yellow), Abdul's unique bird (non-yellow), the Abdul-Mala shared bird (non-yellow), the Abdul-Chetan shared bird (yellow), the Mala-Chetan shared bird (yellow), and the bird all three shared (yellow).

Let's summarize:

• Yellow birds: Chetan's unique bird, Mala's unique bird, the Abdul-Chetan bird, the Mala-Chetan bird, and the all-three bird, which is 5 birds.
• Non-yellow birds: Abdul's unique bird and the Abdul-Mala bird, which is 2 birds.

So in all, 5 yellow birds and 2 non-yellow birds were seen, which is option (2).