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

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