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Each person in a group of 110 investors has investments

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Each person in a group of 110 investors has investments [#permalink]  29 Apr 2018, 11:48
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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
[Reveal] Spoiler: OA

Last edited by Carcass on 29 Apr 2018, 14:09, edited 1 time in total.
Edited by Carcass
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Re: Each person in a group of 110 investors has investments [#permalink]  29 Apr 2018, 14:21
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Of 110 people, we can split them into S +E. Now, of people in equities, 25% have E+S which means 75% have only equities. Of people in securities 40% have S+E, which means 60% have only securities.

Of all this, the question asks for those who have only Equities. So, 75% of 110. The result is 82.5 which is close to answer B.

But the question is not good, it should give us whole numbers.

Hope this helps.

Regards
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Re: Each person in a group of 110 investors has investments [#permalink]  30 Apr 2018, 00:38
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Carcass wrote:
Of 110 people, we can split them into S +E. Now, of people in equities, 25% have E+S which means 75% have only equities. Of people in securities 40% have S+E, which means 60% have only securities.

Of all this, the question asks for those who have only Equities. So, 75% of 110. The result is 82.5 which is close to answer B.

But the question is not good, it should give us whole numbers.

Hope this helps.

Regards

But doesn’t the question says 25% of e only and 40% of s only.which leads to 0.25e=0.4s as it’s the common area and e+s-(0.25e or 0.4s)=110
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Re: Each person in a group of 110 investors has investments [#permalink]  01 May 2018, 05:53
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Expert's post
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
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Re: Each person in a group of 110 investors has investments [#permalink]  05 May 2018, 12:19
Is there enough way to solve such problem using Venn diagram?
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Re: Each person in a group of 110 investors has investments [#permalink]  06 May 2018, 11:03
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awamy wrote:
Is there enough way to solve such problem using Venn diagram?

The mathematics still remain the same. Venn diagram is visually solving the same problem.
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Re: Each person in a group of 110 investors has investments [#permalink]  09 May 2018, 15:03
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Expert's post
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

We can create the equation:

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.

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Re: Each person in a group of 110 investors has investments   [#permalink] 09 May 2018, 15:03
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