But this is NOT a double matrix problem. I do not understand this fixation with the double matrix way to solve

Can you please provide more details in your way of thinking? Can't really get your calculations

If we consider the % as real numbers we do have 82 in category A and 46 in category B

The question asks to you that 128 (A+B= 82+46) is = to 35 of them that trade in BOTH categories. IF 35 trade in both the rest do not trade at all

x/100 of 128 =35

x=3500/128

x=27.3

I hope now is more clear

Hi there, I have looked at this question again but I do not agree with having 27% as a correct answer. I think it's 7.5%. Double matrix method yields 7.5%. Can others also post what you think?

I also think it's A.

but it says % of investors "surveyed" who traded in that category, then how can we jump to the conclusion that its additon = 35%. Actual people who traded in A and B is higher right. I mean say 100 people actually traded in A, then only 82% were surveyed.

At a closer look I also thing tha answer is A

With the formula

A+B-B+N=156

128+70-55+N=156

N=13

What percent of 156000 is 13000

x/100 156000=13000

x=8

The answer should be A

I also think the answer here should be A
Total = A + B - (both A and B) + (neither A nor B)
156000 = 82%*156000 + 45.5%*156000 - 35%*156000 + neither
<=> neither = 11700
=> percent of investors traded in neither of these two categories = 11700/156000 = 7.5%

The answer is A.
82% of the investors traded in A -> 18% of the investors did not trade in A.
45.5% of the investors traded in B and 35% of the investor traded in both A and B -> 10.5% traded in B but not in A.
Therefore, 7.5% traded neither in A nor B (18-10.5).

The way I solve it:
Total = A + B - Both + N
100% = 82% +45.5% - 35% + N (neither)
100% - 92.5% = N
N = 7.5%

This saves time b/c you don't have to convert to # investors, imho

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