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In a battle 70% of the combatants lost an eye, 80% an

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Intern
Joined: 25 Jun 2004
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In a battle 70% of the combatants lost an eye, 80% an [#permalink]  04 Jul 2004, 07:24
In a battle 70% of the combatants lost an eye, 80% an year,75% an arm,85% a leg,x% lost all the 4 limbs. The minimum value of X is

1. 10
2. 12
3. 15
4. None of these

The answer is 10 but how ??
SVP
Joined: 03 Feb 2003
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yeah... a pretty interesting
my solution:

let there be 100 combatants, of which
1) 30 did not lost an eye; therefore, 70 did lost one, of which
2) 20 did not lost an ear; therefore, 50 did lost one, of which
3) 25 did not lost an arm; therefore, 25 did lost one, of which
4) 15 did not lost a leg; therefore, 10 did lost one

Finally, these 10 are the most unlucky ones.
I do not see, however, why this number is minimal. It should be the only solution, no?

BTW, is it possible to calculate the number of people who lost nothing?
Manager
Joined: 01 Jun 2004
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Location: Kiev, Ukraine
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Re: Sets Question [#permalink]  04 Jul 2004, 23:38
khurman wrote:
In a battle 70% of the combatants lost an eye, 80% an year,75% an arm,85% a leg,x% lost all the 4 limbs. The minimum value of X is

1. 10
2. 12
3. 15
4. None of these

The answer is 10 but how ??

It's OK, khurman... Look, if a% of combatants lost something A, and b% of combatants lost something (et's call it B), then AT LEAST (a + b - 100)% of combatants lost both A and B.

Thus, we get that at least 50% = 70 + 80 - 100 lost both an eye and an ear, at least 25% = 50% + 75% - 100% lost an eye, an ear, and an arm, and at least 10% = 25% + 85% - 100% lost an eye, an ear, an arm, and a leg..!

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Four overlapping sets
Senior Manager
Joined: 21 Mar 2004
Posts: 444
Location: Cary,NC
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I had a doubt.....it may be that I am reading too much into the question.

During the last phase where we calculate that

at least
100%-(85%+25%) = 10% lost both an arm and a leg.

however x% is the % who lost all 4 limbs !

the question says 85% lost a leg and 75% an arm....and not 2 legs and 2 arms......am i reading too much here ?

- ash
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ash
________________________
I'm crossing the bridge.........

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