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Question d'entretien d'embauche

Entretien de Analyste Commercial Paris

Si je bois la moitié de ma bouteille de 50 cl, puis je te

  la donne et tu bois la moitié du reste, puis tu me la rends et je bois la moitié de ce qu'il reste, etc. jusqu’à ce que la bouteille soit vide... Finalement quelles seront les quantités totales que
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Réponse de l'entretien

5 réponses

1

Slice the full process in steps:
Step 1: he drinks 100, you 50
Step 2: he drinks 25, you 12.5
etc.
At the end, he will have drunk 2 and you 1. Thus he drank 33.33 cl and you 16.66 cl

Candidat à l'entretien, le 21 nov. 2011
0

for any quantity, the first person gets 2/3, the other 1/3. Because of the 1/2. This could be proven with calculus, or it's pretty easy approximate in your head- you get 1/2 of 25, or 12.5, then the other person has 6.25, then you get 3.1, then they get 1.5, then you get .7. Stop there. You get 12.5 + 3.1 +0.7 or about 16.3 that's pretty obviously about 1/3 of 50. So the other tiny sips would get you there.
Fun problem, actually

scott, le 24 mai 2012
2

Person 1: Drinks 50/2, then 50/8, then 50/32 and so on. It's an infinite suite, the infinite summation gives 50/2*1/(3/4)=100/3 which is 33.33.
Same reasoning for the other person works, but knowing the bottle is 50cl, he drinks 16.66cl.

Etienne, le 27 août 2012
4

You can do it in this way:
1st person drinks: 1/2 + 1/8 + 1/32 +....
2nd person drinks: 1/4 + 1/16 + 1/64+... which is equal to
1/2(1/2 + 1/8 + 1/32 + ). So the second drinks half of what the first drinks. So the first drinks 2/3 50cl and the second1/3 50cl

Lorenzo, le 18 oct. 2013
0

Building on what Lorenzo said and to be 100% rigorous:
a=2b
a+b=50cl

a=2b
3a=50cl
...

Adav, le 13 déc. 2016

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