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

Step 1: Understanding the Question.
Three people go bird watching. Each person sees one bird unique to them, each pair of people shares one bird that the third person does not see, and one bird is seen by all three. That gives 3 unique birds, plus 3 birds shared by exactly two people, plus 1 bird seen by everyone, so there are 3 + 3 + 1 = 7 distinct birds in total. Each person, then, sees their own unique bird, plus the two birds they share with each of the other two people, plus the one bird everyone sees, which is 1 + 1 + 1 + 1 = 4 birds per person.

Step 2: Key Approach.
Label the 7 distinct birds so we can track which ones are yellow. Let a be Abdul's own unique bird, m be Mala's own unique bird, c be Chetan's own unique bird, am be the bird shared only by Abdul and Mala, ac be the bird shared only by Abdul and Chetan, mc be the bird shared only by Mala and Chetan, and x be the one bird all three saw. Then Abdul's four birds are a, am, ac, x, Mala's four birds are m, am, mc, x, and Chetan's four birds are c, ac, mc, x. We use the yellow counts given for each person to figure out which of these seven birds are yellow.

Step 3: Detailed Explanation.
Chetan saw 4 birds, c, ac, mc, x, and all four of them were yellow, since the passage says four of the birds Chetan saw were yellow. So c, ac, mc and x are all yellow.
Abdul saw a, am, ac, x, and only two of these four were yellow. We already know ac and x are yellow from Chetan's list, that already gives two yellow birds in Abdul's set. Since Abdul's total yellow count is exactly two, the remaining two birds in his set, a and am, must both be non-yellow.
Mala saw m, am, mc, x, and three of these four were yellow. We know mc and x are yellow, and we just found that am is non-yellow. That accounts for two yellow birds so far, mc and x, with am confirmed non-yellow. Since Mala's total yellow count is three, the last bird in her set, m, must be yellow to make the count reach three.
So across all seven distinct birds: a is non-yellow, m is yellow, c is yellow, am is non-yellow, ac is yellow, mc is yellow, and x is yellow.

Step 4: Final Answer.
Counting up, the yellow birds are m, c, ac, mc and x, which is 5 yellow birds. The non-yellow birds are a and am, which is 2 non-yellow birds. That matches option (2), 5 yellow birds and 2 non yellow birds.