Arithmetic+ 09 : UNIZOR.COM - Math+ & Problems - Arithmetic

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Arithmetic+ 09

Try to solve this problem without any writing, just in your head.

Problem A

A large water tank is filled to the brim.
It's capacity is unknown.
There are two pipes used to empty this tank.
If only the first pipe is open, the tank will be empty in 14 minutes.
If both pipes are open, the tank will be empty in 10 minutes.
Assume that the speed of the water flow is always constant and depends only on the pipe's diameter.
How long would it take to empty this tank, if only the second pipe is used?

Solution A
An easy way to solve this problem without pen and paper is to see how much water different pipes can let through in the same amount of time.
Let's choose a number divisible by both 14 and 10, like 70.
If a tank can be emptied through pipe #1 in 14 minutes, in 70 minutes this pipe can empty 5 tanks.
Two pipes can let through the water of one tank in 10 minutes. Therefore, in 70 minutes two pipes can empty 7 tanks of water.
So, the pipe #1 in 70 minutes can empty 5 tanks. Both pipes in the same amount of time (70 minutes) can empty 7 tanks of water. Therefore, pipe #2 alone in 70 minutes can empty 7−5=2 tanks of water.
Therefore, one tank the pipe #2 can empty in 70/2=35 minutes.

Answer A
The second pipe can empty the tank in 35 minutes.


Problem B

Mike and David felt like having an ice cream for lunch.
However, it appeared that Mike is short on money. He needed $3 more to buy a single scoop of ice cream.
David looked at his money and it appeared that he is also short by $1 to buy a single scoop of ice cream.
Then they thought to combine their amounts and buy only one scoop to share. Unfortunately, the total was insufficient for a single scoop even then.
How much (in whole dollars) does a scoop of ice cream cost?

Solution B
If Mike had, at least, $1 in his pocket, combined with David's money (who was short by $1), they would be able to buy a scoop of ice cream.
Since they were short even combining their money, Mike's capital was zero dollars.
Therefore, since he was short by $3, the price of a scoop of ice cream was $3.

Answer B
A scoop of ice cream costs $3.


Problem C

There are circles and squares drawn on a sheet of paper.
Some of them are red, the other are blue.
The number of red circles is equal to the number of blue squares.
What is greater, the number of red shapes or the number of squares?

Solution C
The number of red shapes equals to the number of red squares plus the number of red circles.
The number of squares equals to the number of red squares plus the number of blue squares.
The first term of each statement above ("red squares") is the same.
The second term in the first statement ("red circles") equals to the second term in the second statement ("blue squares"). Therefore, the number of red shapes equals to the number of squares.

Answer C
The number of red shapes is equal to the number of squares.