Question 52

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?

Solution

Each of the three persons- Abdul, Mala, and Chetan saw 1 unique birds each. Therefore, the number of unique birds=3.

Each pair of the three persons saw a bird different to the other. Therefore $$^3C_2$$ =3 birds were seen by a pair of two persons each.

Everyone saw a common bird.

Therefore total birds = 7.

Let the birds which were seen by Abdul, Mala, and Chetan uniquely be shown as A, B and C.

Birds seen by Abdul and Mala, Mala and Chetan, Abdul and Chetan be shown as AM, MC and AC respectively.

Birds seen by all of them be shown as AMC.

Birds seen by Abdul are A, AM, AC and AMC

Birds seen by Mala are M, AM, MC and AMC

Birds seen by Chetan are C, AC, AM and AMC.

It is given that Chetan saw 4 yellow birds. So, C, AC, AM and AMC are yellow birds.

For Abdul, it is given that he saw 2 yellow birds only. So, A and AM are non yellow birds, as he already saw AC and AMC.

For Mala, as he saw 3 yellow birds, and MC and AMC are already among the yellow birds seen by him, and since AM is a non yellow bird. Therefore M has to be a yellow bird.

Therefore, in total, there are 5 Yellow birds- M,C, MC, AC, AMC. And the other two- A and AM are non-yellow birds. 


Create a FREE account and get:

  • All Quant Formulas and shortcuts PDF
  • 170+ previous papers with solutions PDF
  • Top 5000+ MBA exam Solved Questions for Free

cracku

Boost your Prep!

Download App