SOLUTION: ``A boss took the poll results from the readership of three newspapers and threw them in the wastepaper basket. Vern was not happy and went to talk with Elsie. �"Why are they wro

Question 789195: ``A boss took the poll results from the readership of three newspapers and threw them in the wastepaper basket. Vern was not happy and went to talk with Elsie.
�"Why are they wrong?" Vern asked Elsie. He handed Elsie his notes. Of those surveyed, 196 read exactly two of the three papers, the bugle, the planet, and the recorder. 673 read only the recorder, while 926 of those who read a paper did not read the planet. 153 of the planet readers read at least one of the other two papers. Of those bugle readers who did not read the planet, �there were 171 more who read the bugle alone than who read the recorder. 210 of the bugle readers read either the bugle alone or else both of the other papers.
After a couple of minutes of reading, elsie found the mistake. Show her work
Also, use a venn diagram

I'm very stressed with this question and I've tried and tried but I'm getting worked up over it. Can someone please help me with this? This is grade 12 data management. This one is oddly very difficult from the other questions.

MY WORK: I keep getting that the mistake Elsie found is that there is not enough information. My problem becomes, how do I show this? Like I know by reading the question that there is not enough information, but how can I show it?

Found 2 solutions by xinxin, KMST:
Answer by xinxin(76) (Show Source): You can put this solution on YOUR website!
First of all, Vern did not specify how many people he surveyed. Additionally, it is hard to calculate this number by using given facts. Second, his notes was in a mess. For example, the 196 people could read either the bugle, the planet or the planet, the recorder or the bugle, the recorder. Finally, the data was contradicted. Vern said "926 of those who read a paper did not read the planet", so the total number of people who read the bugle or the record should be 926. However, he then stated " Of those bugle readers who did not read the planet,there were 171 more who read the bugle alone than who read the recorder." Thus the total number of people who read bugle or the recorder was 673+673+171 = 1517>926 (1517 doesn't take account of people who read both papers).
I can't put a venn diagram in the answer, but it isn't difficult to draw the diagram by yourself.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

There are 7 variables for 7 groups of readers:
B = number of people who read only the Bugle
P = number of people who read only the Planet
R = number of people who read only the Recorder
BP = number of people who read only the Bugle and the Planet
BR = number of people who read only the Bugle and the Recorder
PR = number of people who read only the Planet and the Recorder
BPR = number of people who read all 3 papers

There are 6 equations:
BP + BR + PR = 196 because "196 read exactly two of the three papers"
R = 673 because "673 read only the recorder"
B + R + BR = 926 because "926 of those who read a paper did not read the planet"
B + BPR + PR = 153 because "153 of the planet readers read at least one of the other two papers
B = BR + 171 because "Of those bugle readers who did not read the planet, there were 171 more who read the bugle alone than who read the recorder"
B + BPR = 210 because "210 of the bugle readers read either the bugle alone or else both of the other papers"

With more variables than equations, we cannot solve the system of linear equations for all variables.
However, there is an inconsistency.
There is one subset of equations where we can solve for 3 of those variables.
Among the people who do not read the Planet, we have 3 groups:
those who read only the Recorder,
those who read only the Bugle,
and those who read just the Bugle and the Recorder.
We can find the size of those 3 groups.
-->
So, if B=212, then B + BPR = 210 would require a negative BPR.

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