find minimum percentage

niharika_kumar · 2014-12-30 03:12:30

hi friends.
I am back after few months. Feeling really good to be here again.
How are you all?

So here is my question.

In second world war 70% soldiers lost their left arm, 75% lost their right arm, 80% lost their left eye and 85% lost their right eye.
Find the minimum percent who lost all four parts?

pls help.

Niharika Kumar

Bob · 2014-12-30 22:42:10

hi Niharika,

I'm well; hope you are too.

I haven't met a problem with four sets before so I'm unsure, but, as no one else is having a go, I'll give you my attempt. I cannot see anything wrong with it but you'll have to judge for yourself.

When I encounter a tricky question, I try a simplified version first. So I looked at the two set problem above. What's the minimum b ?

We have these constraints:

a + b + c + d = 100

a + b = 70

b + c = 75

a + d = 25

c + d = 30

These are not all independent of each other but you can eliminate two unknowns:

b = 100 - a - c - d = 100 - (25 - d) - (30 - d) - d = 45 + d

As d ≥ 0 => b ≥ 45

You can get similar limits on b using other pairs of sets but 45 is the lowest.

So, is it possible to draw a four set diagram with the intersection of all four being 45 ?

Well it was tough just making a venn diagram with all 16 regions but I eventually managed by making the fourth set wiggle all around the other three. You'll have to try making your own. But I did find numbers to put in all the regions, with 45 in the middle. So it is possible and some other regions were forced to be zero, so I think 45 is the minimum.

Bob

ps. Your questioner is a bit morbid, don't you think ? Plenty of ways to make this problem without all that mutilation.

pps. Just had second thoughts so I might have another go at this.

niharika_kumar · 2014-12-31 02:15:59

well there was a solution too which he gave.
But that solution is not being digested by me.
The answer is 10%.
And the solution said that convert the percentage to the opposite of what it said. for example: If 70% have lost their left hand then there are 30% who have not lost it.And do the same with others.Then he added all these data claiming that maximum percentage who didn't loose any part is 90% ,hence minimum percentage who lost all parts is 100-90=10%.

When I asked him if the data would have been given like 50% each,he told me there won't be such question.

help.

Bob · 2015-01-01 01:43:02

That sounds more like it. I'll give it some thought and come back later.

Bob

Bob · 2015-01-02 02:34:23

hi Niharika,

So my earlier answer was completely wrong. Sorry about that.

Using the answer from your post 3, I now have a diagram that explains why this method works. I'll post it if you wish.

Bob

niharika_kumar · 2015-01-02 03:15:16

please post it.

Bob · 2015-01-02 07:33:27

hi Niharika,

It is quite difficult to make a diagram with 4 overlapping sets, showing all 16 regions. I did manage one but I had to make a very wobbly outline to the fourth set. This diagram is simpler but two regions are missing; g ={points in A and D but not in C nor B} and h = {points in B and C but not in A nor D}

So the regions outside the sets are

A' = {b,c,d,h,i,j,n}
B' = {a,c,d,f,g,j,m}
C' = {a,b,d,e,g,i,L}
D' = {a,b,c,e,f,h,k}

So the specified calculation works out

100 -(A'+B'+C'+D') = p -2a-2b-2c-2d-e-f-g-h-i-j

We can make p as small as possible by choosing zeros for all those other regions ie. a=b=c=d=e=f=g=h=i=j=0

This leaves the diagram like this:

You can see that the total for each set is correct (eg. A = 15+20+25+10=70)

Bob

Math Is Fun Forum

#1 2014-12-30 03:12:30

find minimum percentage

#2 2014-12-30 22:42:10

Re: find minimum percentage

#3 2014-12-31 02:15:59

Re: find minimum percentage

#4 2015-01-01 01:43:02

Re: find minimum percentage

#5 2015-01-02 02:34:23

Re: find minimum percentage

#6 2015-01-02 03:15:16

Re: find minimum percentage

#7 2015-01-02 07:33:27

Re: find minimum percentage

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