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Bunuel
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Every manager in a certain brokerage firm has an intellectual coacher 30 Jun 2022, 20:30
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Difficulty:

25% (medium)

Question Stats:

75% (02:18) correct 25% (02:31) wrong based on 53 sessions

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Every manager in a certain brokerage firm has an intellectual coacher or an emotional coacher or both. The number of managers that do not have an emotional coacher is half the number of managers that have both an emotional coacher and an intellectual coacher. 9 managers do not have an emotional coacher. If the total number of managers that have an emotional coacher is 12 greater than the number of managers that have both kinds of coachers, then how many managers are there in that brokerage firm?

A. 30
B. 33
C. 36
D. 39
E. 48
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D
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Every manager in a certain brokerage firm has an intellectual coacher 30 Jun 2022, 20:49
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Bunuel
Every manager in a certain brokerage firm has an intellectual coacher or an emotional coacher or both. The number of managers that do not have an emotional coacher is half the number of managers that have both an emotional coacher and an intellectual coacher. 9 managers do not have an emotional coacher. If the total number of managers that have an emotional coacher is 12 greater than the number of managers that have both kinds of coachers, then how many managers are there in that brokerage firm?

A. 30
B. 33
C. 36
D. 39
E. 48
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Bunuel

Hey Bunuel, I solved using Vein Diagram. Is there any effective way/method 2 to solve this?
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Every manager in a certain brokerage firm has an intellectual coacher 30 Jun 2022, 21:26
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Bunuel
Every manager in a certain brokerage firm has an intellectual coacher or an emotional coacher or both. The number of managers that do not have an emotional coacher is half the number of managers that have both an emotional coacher and an intellectual coacher. 9 managers do not have an emotional coacher. If the total number of managers that have an emotional coacher is 12 greater than the number of managers that have both kinds of coachers, then how many managers are there in that brokerage firm?

A. 30
B. 33
C. 36
D. 39
E. 48
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9 do not have E.
The number that do not have E is half the number that have both. 18 have both.
The total that have E is 12+18 = 30.

9 do not have E. 30 have E. That means 39.

Answer choice D.
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