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In a war, 70% of soldiers lost one eye, 80% an ear, 75% an arm : Quantitative Comparison Questions

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Re: In a war, 70% of soldiers lost one eye, 80% an ear, 75% an arm [#permalink]
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KarunMendiratta wrote:
Explanation:

Soldiers who lost one eye and an ear = 70 + 80 − 100 = 50%
Soldiers who lost one eye, an ear and an arm = 50 + 75 − 100 = 25%
Soldiers who lost one eye, an ear, an arm and a leg = 25 + 85 − 100 = 10%

Therefore, Soldiers who lost all the four limbs = 10%

Col. A: 10
Col. B: 10

Hence, option C

only arms and legs are counted as limbs.
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In a war, 70% of soldiers lost one eye, 80% an ear, 75% an arm [#permalink]
1
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Follow the explanation together with the pic so things make more sense.

I saw this method on gmat prep club when working with overlapping set questions.
You use a bar graph from 0 to 100 percent.

Then you fill up the space always trying to avoid overlap as much as possible.

First group of 85% we covered 0 to 85

Second group of 80% we covered from 100 to 20 --> at this point we have an overlap of 65% (20 to 85)

Third group of 75% we covered 0 to 20, then 85 to 100, and we are left with a total of 40 (from 20 to 60) that we must overlap with the other two groups ---> three-way overlap of 40%

Fourth group of 70% we cover 0 to 20, 60 to 100, and then a remainder of 10% that we must include in the overlap of all 4 categories.

So minimum intersection of all 4 groups is 10%

Final Answer: C
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minimizing overlap of 4 categories.png
minimizing overlap of 4 categories.png [ 16.58 KiB | Viewed 3048 times ]

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Re: In a war, 70% of soldiers lost one eye, 80% an ear, 75% an arm [#permalink]
2
To find the minimum value of

x (percentage of soldiers who lost all four limbs), we need to consider the worst-case overlap of these injuries. The maximum percentage of soldiers who could have avoided losing all four limbs is the sum of the smallest percentages of soldiers who did not lose each limb:

30% did not lose an eye (100% - 70%)
20% did not lose an ear (100% - 80%)
25% did not lose an arm (100% - 75%)
15% did not lose a leg (100% - 85%)
If we assume these groups are entirely distinct (which gives the minimum overlap), then the maximum percentage of soldiers who did not lose all four limbs is the sum of these percentages:

30
%
+
20
%
+
25
%
+
15
%
=
90
%
30%+20%+25%+15%=90%

Therefore, at least 10% of the soldiers must have lost all four limbs to account for all possibilities. This gives us the minimum value of

x.
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Re: In a war, 70% of soldiers lost one eye, 80% an ear, 75% an arm [#permalink]
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