Every manager in a certain brokerage firm has an

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Every manager in a certain brokerage firm has an

by AAPL » Tue May 01, 2018 4:58 am

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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

The OA is D.

Is there an approach to this question? Can anyone help, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Tue May 01, 2018 4:58 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue May 01, 2018 6:31 am

AAPL wrote: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

The OA is D.

Is there an approach to this question? Can anyone help, please? Thanks!

I'd draw a Venn diagram with two circles overlapping. Label the one circle Intellectual, the other Emotional.

Call the area for Intellectual A, the overlapped area B and Emotional C.

Translate the first statement: Not having an Emotional coach leaves only A. The members with both coaches is B, so

A=B/2

9 managers without an Emotional coach means A = 9, so B =18.

The total number with an Emotional coach is B + C and that is equal to B + 12, so C must = 12.

So, A = 9, B= 18 and C=12. Adding equals 39, D

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed May 02, 2018 9:29 am

AAPL wrote: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

We are given that 9 managers do not have an emotional coacher and that is half the number of managers who have both an emotional coacher and an intellectual coacher. Thus, the number of managers who have both kinds of coachers is 9 x 2 = 18.

We are also given that the number of managers who have an emotional coacher is 12 greater than the number of managers who have both kinds of coachers. Thus the number of managers who have an emotional coacher is 18 + 12 = 30.

Since every manager either has an emotional coacher or (s)he doesn't, then the total number of managers must be 30 + 9 = 39. (Note: for those who don't have an emotional coacher, they must have an intellectual coacher.)

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]