I took nearly 5 minutes for this one

Question

I took nearly 5 minutes for this one.

AJB77 · Answer

Sparky,

Please give some explanations.

Others - please show work as well.

sparky · Answer

2) is suff.
100-30=70% like at least one, 40% like Mega, 30% like Jumbo so none like both Mega and Jumbo

1) insuff
 
there are 9 possible outcomes for how each individual would vote
call them x1...x9 9 unknowns

however we can construct only 6 equations 
if we know that 10% both dislike J and M, we know only 1 unknown

we still are left with 2 extra variables that cannot be solved for

AJB77 · Answer

Sparky,

Can you explain a bit more on the part about 9 variables?

Thanks

sparky · Answer

for example,

for people who are indifferent to Jumbo cola
40 = x1+x2+x3
x1- Mllike Jindiff
x2 - Mdisllike Jindiff
x3 = M indiff J infiff

do the same for each percent entry in the table

NM · Answer

Out of these 70%, couldn't some be  indifferent  to either cola?

AJB77 · Answer

Thanks sparky.

Is there a good book/site where there are many questions similar to this? I feel that Set theory is one of my last frontiers.

ssap · Answer

When 30% of the people don't answer 'like' for either Mea or Jumbo, this by itself includes both 'dislike' and 'indifferent' categories.
So 70% is just those who like either of the brands.



Good explanation Sparky.

rchadha · Answer

Are there other approaches to this qs?

rchadha · Answer

I don't understand the construction od equation piece in Sparky's explan.

HongHu · Answer

(1) 10% dislike both, so 45% dislike one or the other (35%+20%-10%). In other words, 55% like or is indifferent toward both Maga and Jumbo. However there's no sufficent data for us to separate the ones who like and the ones who is indifferent.

(2) 30% don't like either one. That means 70% likes one or the other. But from the chart there could be only 70% people who likes one or the other in the maximum, this is when 40% likes Jumbo and not the Mega, and 30% likes Maga and not Jumbo. Sufficient to tell that 0% people like both Maga and Jumbo.

rchadha · Answer

That explains! Thanks! I guess one doesn't need to go any further than that on a DS qs!

I took nearly 5 minutes for this one

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