Sets Question

Lex Luthor

anybody throw their eye over this, no matter how many times I work it out, I still get same answer for x which is 15

However when I put the value of x (15) back in, I get a negative number for one of the groups

Muhammed_1

The number of people who said they disliked all fruits is 4x, not just 4 people.

It's a fairly hard problem... but maybe I'm missing something.




...
I've run into a problem.

Muhammed_1

I've now successfully solved it but I didn't get an integer value for x. That was the problem I had earlier.

The answer does work though even with the non integer value for x.

x = 1.8
4x, who dislike all fruit = 7.2

Lex Luthor

My apologies, the value of x=15 is from another question I was doing

I also got x=1.8 for this one. Have gone over it many times and still come up with same answer. Good to know I'm not going crazy if someone else is getting same

Lex Luthor

Muhammed_1 wrote: »

The number of people who said they disliked all fruits is 4x, not just 4 people.

It's a fairly hard problem... but maybe I'm missing something.



...
I've run into a problem.

Just been told there is a typo in the question, its 2x, not 4x, therefore the value of x=3 and it works out

Muhammed_1

Yes, I was also thinking after that if it was 4 people, and not 4x people, that x would be 5, and it'd work out with integer values.

It'd be a bit unfair to have a question like that on an exam because of the non-integer answer.

evolving_doors

Lex Luthor wrote: »

Just been told there is a typo in the question, its 2x, not 4x, therefore the value of x=3 and it works out

I dunno, I just took the values from the question you posted and got x=15 !

Edit: Sorry just realised then P only would have to be -1

It's kind of gratifying discovering that the person setting the question made a mistake. It just makes you have to trust yourself even more. I suppose if it were in an exam though you might waste a lot of time double checking a bad question.

Muhammed_1

Thinking about this again it's a serious flaw in the question, to have a non-integer answer.

It's Sets!

The whole point is to have whole numbers of objects in each set. Having fractions of objects in a set is fairly unusual I'd have thought and maybe it never happens.

If it never happens then the non-integer answer is a bigger problem.

Lex Luthor

Gebgbegb wrote: »

I dunno, I just took the values from the question you posted and got x=15 !

Edit: Sorry just realised then P only would have to be -1

It's kind of gratifying discovering that the person setting the question made a mistake. It just makes you have to trust yourself even more. I suppose if it were in an exam though you might waste a lot of time double checking a bad question.

I'll show my workings out in a while and put it up, think I got x=3 but will double check

Lex Luthor

My workings...

Yakuza

2x instead of 4x makes more sense, as when you work out all the various combinations, you end up with 241+3x = 250, making an integer solution for x.

P = 124, G = 101, K = 147

K ∩ P ∩ G = x
(K ∩ P) \ G = 72 - x
(G ∩ P) \ K = 38 - x
(K ∩ G) \ P = 21 - x
P \ (G ∪ P) = 14 + x : (124 - ((72-x)+x+(38-x))
G \ (K ∪ P) = 42 + x : (101 - ((38-x)+x+(21-x))
K \ (G ∪ P) = 54 + x : (147 - ((21-x)+x+(72-x))
No set : 2x.

This totals to 241 + 3x, which must be 250, x is 3 and you get sensible answers in the Venn diagram.
Bad form to have a typo -was that a textbook or an exam?

Lex Luthor

Yakuza wrote: »

2x instead of 4x makes more sense, as when you work out all the various combinations, you end up with 241+3x = 250, making an integer solution for x.

P = 124, G = 101, K = 147

K ∩ P ∩ G = x
(K ∩ P) \ G = 72 - x
(G ∩ P) \ K = 38 - x
(K ∩ G) \ P = 21 - x
P \ (G ∪ P) = 14 + x : (124 - ((72-x)+x+(38-x))
G \ (K ∪ P) = 42 + x : (101 - ((38-x)+x+(21-x))
K \ (G ∪ P) = 57+ x : (147 - ((21-x)+x+(72-x))
No set : 2x.

This totals to 241 + 3x, which must be 250, x is 3 and you get sensible answers in the Venn diagram.
Bad form to have a typo -was that a textbook or an exam?

Ya agree with you, got same answer as per my workings when No Set =2x

The typo was in an exam book

There is another one that has us debating aswell, see attached

I've also included my workings. The text book says X=6, but I got x=3

The debate is over the value of owning an MP3 & Smartphone but not an ipod.

Yakuza

I agree with you. If the last information piece read "25 own an iPod and a smartphone but not an MP3 player" then 6 would be correct.

Muhammed_1

Hmmm.

I got x=6.

But then I have a negative number of people owning smartphones!


edited to add:
In your workings for Set 7 you have drawn the Venn diagram correctly but you must have made a error in your calculations.

25-x is correct for Ipod intersects Smartphone but excludes MP3.

The Venn diagram adds up to 96 - x which equals 90.
x= 6

Muhammed_1

bizarre double post.

I have found your error.

At the end of your calculation you have

..+ 2x + x = 109

That 2x should be 3x. You calculation would then be correct.

You should follow a consistent pattern when adding up the Venn diagram. So, left to right, and top to bottom.

You went left to right, then down, and right to left, then down. Complicated, and it led to your error.

Lex Luthor

Muhammed_1 wrote: »

bizarre double post.

I have found your error.

At the end of your calculation you have

..+ 2x + x = 109

That 2x should be 3x. You calculation would then be correct.

You should follow a consistent pattern when adding up the Venn diagram. So, left to right, and top to bottom.

You went left to right, then down, and right to left, then down. Complicated, and it led to your error.

Nice one, thanks for finding my error, not sure how I made that mistake as I had worked it out previously and got x=6

So X=6 which is the correct value for X, but when you put in that value of x into the Venn Diagram, you get a negative value for the Smartphone Only section

14-3x
14-3(6)
14-18
-4

I think this is where it all went Pete Tong the last time. We were able to get x=6, but then we got this negative value

Lex Luthor

Muhammed_1 wrote: »

You should follow a consistent pattern when adding up the Venn diagram. So, left to right, and top to bottom.
.

Thanks for this tip, will let my boys know this and hopefully help them