In a certain school of dolphins, 20 dolphins eat neither sardines nor tuna. 50 of the dolphins do not eat tuna, and 60 eat sardines. Which of the following statements regarding the school of dolphins is possible?

A. 10 dolphins do not eat sardines.
B. 20 dolphins eat both sardines and tuna.
C. 40 of the school dolphins that do not eat tuna, eat sardines.
D. There are 70 dolphins in the school.
E. 30 of the dolphins eat tuna.

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Hi Bunuel,

Could you please explain why B is incorrect?

If we set up an above matrix, there are 30 dolphins who eat both tuna and sardine. So we can conclude that 20 in 30 dolphins eat both tuna and sardine. I'm quite confused.

This is what is given:


60 dolphins (green + yellow regions) => Eat sardines
Eat Both = 60 - 30 (Yellow) = 30 (green region)

A. 10 dolphins do not eat sardines.
Incorrect. We know that 20 eat neither. So this is not possible.

B. 20 dolphins eat both sardines and tuna.
Incorrect. We got that eat both = 30

C. 40 of the school dolphins that do not eat tuna, eat sardines.
Incorrect. 30 of those that do not eat tune, eat sardines (the yellow region).

D. There are 70 dolphins in the school.
Incorrect. No tuna = 50 and eat both = 30 so there must be at least 80 dolphins.

E. 30 of the dolphins eat tuna.
30 eat both. It is possible that 30 only eat tuna and there is no dolphin that eats only tuna.

Answer (E)
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