Question: 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

Correct Answer: B

Solution and Explanation:

Approach Solution 1:
According to the conditions,
0.25E=0.4S
E=1.6S

Only equities= 1.6S−1.6S∗0.25=1.2S
Only securities= S−0.4S=0.6S
Both E and S= 0.4S

1.2S+0.6S+0.4S=110
S=50
E=50∗1.6=80

Approach Solution 2:
Total = equities + securities - both
Let’s let s = the number of investors in securities and e = the number of investors in equities. We know that:
0.4s = 0.25e = both; thus:
40s = 25e
8s = 5e
8s/5 = e

Substituting, we have:
Total = equities + securities - both
110 = 8s/5 + s - 0.4s
110 = 8s/5 + s - 2s/5
110 = 6s/5 + s
110 = 11s/5
550 = 11s
50 = s
So e = 8(50)/5 = 400/5 = 80

Approach Solution 3:
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.

b/b+e= 0.25 or e=3b
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

“Each person in a group of 110 investors has investments in either”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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