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Flashcards in Raciocínio Deck (22)
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Estime o faturamento de um posto de gasolina?



Combinação Simples

Na combinação simples, a ordem dos elementos no agrupamento não interfere. São arranjos que se diferenciam somente pela natureza de seus elementos.

C= n! / p!(n-p)!

- formação de equipes


Combinação Composta

Essa combinação também é conhecida como sendo combinação com repetição.

C= (n+p-1)! / p! (n-1)!

- combinação de bolas de sorvete



Arranjos são agrupamentos nos quais a ordem dos seus elementos faz a diferença.

A= n! / (n-p)!

- anagramas
- ocupação de cargos diferentes


Progressão Aritmética

e soma dos termos da PA

an = a1 + (n - 1) . r

S= (a1 + an) * n / 2



an = a1 . q(n-1)


If there is a lily pad in a pond, and it doubles in size every minute and will completely cover the pond in one hour, how long will it take to cover a quarter the pond?

Given that the pond will be covered in one hour and that it doubles in size every minute, at one minute prior to the hour the pond would be half covered. Continuing this line of thought, if we go back another one minute, the pond would be a quarter covered, so the answer is 58 minutes.


Quantas semanas tem em um ano?



How many hairstylists or barbers do you estimate there are there in this city? Explain your logic/assumptions

Explain the logic based on the population of the city, average number of cuts people have per year, number of cuts one barber can do per year, and thus how many that implies there must be. (e.g., 2 million people, each get an average of 4 cuts per year, which results in 8 million cuts per year. Each barber works an average of 8 hours per day, times five days per week, times fifty weeks per year equals 2,000 hours of cutting time per year. Each haircut takes 1 hour. Thus, 8 million haircuts, equal 8 million hours, divided by 2,000 hours per barber requires 4,000 barbers in the city.)


A windowless room contains three identical light bulbs. Each light is connected to one of three switches outside of the room. Each bulb is switched off at present. You are outside the room, and the door is closed. You have one, and only one, opportunity to flip any of the external switches. After this, you can go into the room and look at the lights, but you may not touch the switches again. How can you tell which switch goes to which light?

Switch on switches 1 & 2, wait a moment and switch off number 2. Enter the room. Whichever bulb is on is wired to switch 1, whichever is off and hot is wired to switch number 2, and the third is wired to switch 3


A farmer needs to cross the river with his fox, his chicken and a bag of corn. However, the boat can only fit the farmer and one other thing at a time. The problem is, the fox and the chicken are both hungry, so if he leaves the fox and chicken together, the fox might eat the chicken. If he leaves the chicken and corn together, the chicken might eat the corn.

First, the farmer should take the chicken across. Then, he can go back for the fox. When he arrives at the other side to drop off the fox, he can take the chicken back with him to get the corn. The farmer drops off the chicken and transports the corn to the other side of the river. Finally, the farmer goes back for the chicken and continues to the other side of the river with nothing eaten.


If you have a three-gallon jug and a five-gallon jug, how can you measure out exactly four gallons of water?

First, I would fill the three-gallon jug completely and pour it into the five-gallon jug. Next, I'd fill the three-gallon jug again, and fill the five-gallon jug all the way up to capacity. Since the five-gallon jug is already holding three gallons in it, the three-gallon jug will have one gallon of water remaining in it. Then, I'd empty the full five-gallon jug and pour the one gallon of water I saved into it. Finally, I'd fill the three-gallon jug completely and add it to the gallon of water in the five-gallon jug, resulting in a total of four gallons.


How many ping pong balls can you fit into a Boeing 747? (not the exact answer)

First, I need to know the volume of a ping pong ball, as well as the volume inside a Boeing 747. Knowing this information, I can then divide the volume of the plane by the volume of one ping pong ball. This will result in an approximate amount of ping pong balls that would fit inside the plane


How many pennies, if they are stacked on top of each other, will it take to reach the top of the Empire State Building? (not the exact answer)

first, I need to know how tall the Empire State Building is, as well as how tall a penny is when it's laying flat. Assuming one penny is a 1/4 inch high, I can divide the height of the building by the height of the penny to get the number of pennies I'll need to stack.


You’re about to board a train from London to Newcastle.
You want to know if it’s raining, so you call your three friends who live in Newcastle.
Each friend has a 2/3 chance of telling you the truth and a 1/3 chance of telling you a lie.

All three friends tell you that, yes, it’s raining in Newcastle.

What is the probability that it is, in fact, raining in Newcastle?

You only need one friend to be telling the truth. So if you calculate the odds of them all lying, that’s 1/3 multiplied together, making 1/27 (1/3 x 1/3 x 1/3).

So that’s a 1 in 27 chance that all of your three friends are lying. So, switch that around, and it’s a 26/27 chance one of them is telling the truth – or 96% - that it is, indeed raining in Newcastle!


A snail sits at the bottom of a 30-foot wall.
Each hour it can climb three feet, but it then slips down two feet.
How long does it take the snail to reach the top?

The answer is 28 hours.

That’s because for the first 27 hours it climbs a net one foot. But in the 28th hour, it reaches the top with its three-foot climb before having the chance to slide down two feet.


A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at your head and shoots. *click* You’re still alive. He then asks you, “do you want me to spin it again and fire or pull the trigger again right away?” For each option, what is the probability that you’ll be shot?

The key hint here is that the bullets were loaded adjacent to each other.

There are 4 ways to arrange the revolver with consecutive bullets so that the first shot is blank. These are the possible scenarios:

The other two scenarios would have meant you got shot on the first attempt. (BBxxxx) or (BxxxxB)

Now look at the second slot in those 4 possible scenarios above. Your odds of getting shot are 1/4 or 25%. (Only #1 would get you shot)

But if you respin… there are 2 bullets remaining and 6 total slots. 2/6 or 33%.


There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of its box. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

Go to the box labeled “Apples + Oranges.” Since the label is wrong, it must have one or the other.

This is the box to take one piece of fruit from. Whichever comes out is what that box contains. If you took out an apple, the box has only apples. If you took out an orange, vice versa.

Here’s where it gets tricky a bit tricky. But we’re almost done…

Let’s say you grabbed an apple. Move the “Apples” label over to that box. Now it’s correctly labeled.

You know the “Oranges” box is still labeled wrong (because all 3 were labeled wrong to start and you haven’t touched it). And you know it’s not “Apples”.

So it has to be “Apples + Oranges”. And The last box is “Oranges”.

The same process above would work if you had pulled out an orange at the start.


What is the sum of numbers from 1 to 100?

The trick here is that you have 50 pairs which each sum to 101 (e.g. 1+100, 2+99, 3+98, etc.). So, 50 times 101 = 5050.


Four investment bankers need to cross a bridge at night to get to a meeting. They have only one flashlight and 17 minutes to get there. The bridge must be crossed with the flashlight and can only support two bankers at a time. The Analyst can cross in 1 minute, the Associate can cross in 2 minutes, the VP can cross in 5 minutes and the MD takes 10 minutes to cross. How can they all make it to the meeting in time?

First, the Analyst takes the flashlight and crosses the bridge with the Associate. This takes 2 minutes. The Analyst then returns across the bridge with the flashlight taking 1 more minute (3 minutes passed so far). The Analyst gives the flashlight to the VP and the VP and MD cross together taking 10 minutes (13 minutes passed so far). The VP gives the flashlight to the Associate, who recrosses the bridge taking 2 minutes (15 minutes passed so far). The Analyst and Associate now cross the bridge together taking 2 more minutes. Now, all are across the bridge at the meeting in exactly 17 minutes. Note, that instead of investment bankers, you’ll often see the same question using members of musical bands (usually either the Beatles or U2)


You are given 12 balls and a scale. Of the 12 balls, 11 are identical and 1 weighs slightly more. How do you find the heavier ball using the scale only three times?

First, weigh 5 balls against 5 balls (1st Use of Scale). If the scale is equal, then discard those 10 balls and weigh the remaining 2 balls against each other (Second Use of Scale). The heavier ball is the one you are looking for.

If on the first weighing (5 vs 5), one group is heavier, then of the heavier group weigh 2 against 2 (2nd Use of Scale). If they are equal, then the 5th ball from the heavier group (the one not weighed) is the one you are looking for. If one of the groups of 2 balls is heaver, then take the heaver group of 2 balls and weigh them against each other (Third Use of Scale). The heavier ball is the one you are looking for.


Monte Hall