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In a certain school of dolphins, 20 dolphins eat neither

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In a certain school of dolphins, 20 dolphins eat neither  [#permalink]

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New post 30 Jan 2014, 02:00
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E

Difficulty:

  65% (hard)

Question Stats:

61% (02:25) correct 39% (02:39) wrong based on 125 sessions

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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.

PS: Do not attempt the question if you are planning to take Economist Gmat Tutor free Simulation test.

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Re: In a certain school of dolphins, 20 dolphins eat neither  [#permalink]

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New post 30 Jan 2014, 02:23
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WoundedTiger wrote:
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.

PS: Do not attempt the question if you are planning to take Economist Gmat Tutor free Simulation test.


Set a matrix:
Attachment:
Untitled.png
Untitled.png [ 4.58 KiB | Viewed 2431 times ]
As you can see only E is possible: if there are 0 dolphins who eat tuna but do not eat sardines, then 30 of the dolphins eat tuna (first row).

Answer: E.
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Re: In a certain school of dolphins, 20 dolphins eat neither  [#permalink]

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New post 10 Apr 2019, 00:54
Bunuel wrote:
WoundedTiger wrote:
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.

PS: Do not attempt the question if you are planning to take Economist Gmat Tutor free Simulation test.


Set a matrix:
Attachment:
Untitled.png
As you can see only E is possible: if there are 0 dolphins who eat tuna but do not eat sardines, then 30 of the dolphins eat tuna (first row).

Answer: E.


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.
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Re: In a certain school of dolphins, 20 dolphins eat neither  [#permalink]

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New post 25 May 2019, 01:50
Solution with detailed explanation is attached.
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Re: In a certain school of dolphins, 20 dolphins eat neither  [#permalink]

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New post 25 May 2019, 03:24
WoundedTiger wrote:
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.

PS: Do not attempt the question if you are planning to take Economist Gmat Tutor free Simulation test.


This is what is given:

Attachment:
Screenshot 2019-05-25 at 15.49.53.png
Screenshot 2019-05-25 at 15.49.53.png [ 43.63 KiB | Viewed 214 times ]

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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Re: In a certain school of dolphins, 20 dolphins eat neither   [#permalink] 25 May 2019, 03:24
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