Three competing juice makers conducted a blind taste test with mall

How it could be that 700 shoppers liked brand L and the total number of shoppers who took the taste test is 600?
Ghost shoppers?

This is what I did.

Add J+K+L (100+200+700) = 1000
Then, deduct the shoppers that liked exactly 2 juices = 300
Then, deduct the shoppers that like all 3 (50) however you have to multiply this number by 2, as they have been counted twice in the singular (J+K+L) count.

100+200+700-300-100=600

Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?

A. 1,300
B. 1,000
C. 900
D. 700
E. 600

Solution:
Here,
A (Brand J) = 100
B (Brand K) = 200
C (Brand L) = 700

Exactly Two = 300
All three = 20

Neither = 0



**Formula
All = A + B + C – Sum of exactly two groups – 2*All Three + Neither
= 100 + 200 + 700 – 300 -100 +0
= 600
Answer:600(E)

the question is wrong I think , as 300 shoppers like exactly 2 brands yet a+b-2*all 3=200
so there could only be 200 shoppers who liked exactly 2 brands . and how can 700 people like brand 3 if total shoppers is 600?

That 700 includes all who like brand L including people who like 2 brands and all 3 brands. This can be expressed using a Venn Diagram as shown in the attachment.

the question is still wrong I think ? as there is only 600 people and why would you count 1 people twice is beyond me.