请教解法，答案不明白，谢谢高手

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In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? A) 5 B) 10 C) 15 D) 20 E) 25 答案说是B

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all dislike : 15% Like 1 : 50% Like 2 : 30% Like 3 : 20% You could draw 3 circles , and they will have overlapped area . In Like 1 area , you could separate : Like 1 only : a% , Like 1&2 : d% , Like 1&3 e% In Like 2 area : Like 2 only : b% , Like 2&3 f% In Like 3 area : Like 3 only : c% So you will have 6 variables : a/b/c/d/e/f And you will get 4 equation : a+d+e+5=45 ; b+d+f+5=30 ; c+e+f+5=20 ; a+b+c+d+e+f+5=85 For the first 3 equation , you could choose 2 of 3 add together , and use the last equation to minus , you will get a-f=40 ; c-d=10 ; b-e=20 Then you could substitue a/b/c with f+40/e+20/d+10 into the last equation You will get 2(d+e+f)=10 , so you will know d+e+f+5=10%--Ans