Problem Solving

Source: Princeton Review

A total of 120 investment advisors work at a particular financial services firm, 30 in bonds and the rest in equities. Fifty percent of the investment advisors are board-certified. If one-third of the equities advisors are board-certified, how many bonds advisors are not board-certified?

A. 0
B. 10
C. 15
D. 20
E. 30

The OA is A.

Let us term Investment advisors as IA, Equity Advisors as EA, Bond Advisors as BA and prefix for Board Certified as C
As per the question,
We have: IA = 120
BA = 30 -- (1)
EA = 120 - 30 = 90

As mentioned, fifty percent of the investment advisors are board-certified.
==> 50% of IA = IAC or
==> IAC = 60
Also, given that one-third of the equities advisors are board-certified
==> (1/3)*EA = EAC
==> EAC = 30
We have to find how many bonds advisors are not board-certified or (BA - BAC)
Since, Certified Investment advisors = Certified equities advisors + Certified bonds advisors
==> IAC = EAC + BAC
==> 60 = 30 + BAC
==> BAC = 30 ---- (2)

From (1) and (2), bonds advisors are not board-certified or (BA - BAC) = 0

Correct Answer is A