awamy wrote:

Each person in a group of 110 investors has investments in either equities or securities or both. Exactly 25% of the investors in equities have investments in securities, and exactly 40% of the investors in securities have investments in equities. How many have investments in equities?

A) 65

B) 80

C) 120

D) 135

E) 150

Let the number of people with investment in only securities be \(s\) and only in equity be \(e\) and both equity and security be \(b\).

We know that 25% of investors of equity have investment in secuity and 40% of security investors have equity.

\(\frac{b}{b+e}=0.25\) or \(e=3b\)

\(\frac{b}{b+s}=0.4\) or \(s=1.5b\).

Also there are 110 in total so \(s+e+b=110\). Substitute b from other equation

b=20 and e=60 and s=30.

How many have investments in equities? = e + s =80

_________________

Sandy

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