Ol-maths quiz level-1

Assessment-quiz, level I

Do not use anything but your knowledge, pen and paper. This quiz has only one purpose: give you a suggestion on which course to do.

Just in case, there might be several correct answers to the question. You need to select all of them to get the question right!

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There are three steaks that Jeeves wants to fry. It takes 5 minutes to fry one side of a steak. Jeeves has a pan that can fit at most two steaks at the same time. What is the least amount of time does he need to fry all 3 steaks from both sides? (neglect the time need to turn the steaks)

5 minutes

Not possible... At least 15 minutes is necessary

10 minutes

Not possible... At least 15 minutes is necessary

15 minutes

If you first fry only one side of steaks #1 and #2, then fry only one side of steaks #2 and #3 and then fry only one side of steaks #3 and #1 you will spend 15 minutes all together.

20 minutes

You can do better than 20 minutes

25 minutes

You can do better than 25 minutes

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Once Alice told me that "It was raining everyday last week!". But as it turned out, it was a lie. What statement should I make about the weather last week?

It was not raining at all

No that is not the right conclusion. What if it rained only once last week? Would it still mean that Alice lied?

It was raining on Tuesday

It was sunny every single day

There was at least one day when it was not raining

Yeap, at least one rain-free day is the conclusion you should make

London is the capital of Great Britain

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Which of the following claims are true? Remember to select all that are correct!

The product of two even numbers is always even

If the sum of two integers is odd, then their product is even

The sum of 7 odd numbers is always odd

If the sum of three numbers is odd, then all of them must be odd

If you multiply together several odd numbers then you must get an odd number

If you divide an even number by 2 then you will always get an odd number

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There are three jars. One of them contains tea, one of them contains coffee and one of them contains tea and coffee. One day little boy Tuberg decided to add labels to these jars: one of the labels is "tea", another one is "coffee" and the third one is "tea and coffee" (see the picture). It turned out that all the labels are wrong. Knowing this, in which jar there is tea?

Definitely in the jar with the label "tea"

Definitely in the jar with the label "coffee"

Definitely in the jar with the label "tea and coffee"

It can be in any jar, all the options are possible!

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A group of friends once went on a 3-day trip. During the second day they walked 10 more kilometres than during the first day. And during the third day they walked 2 times more kilometres than during the first day. How many kilometres did they walk during the first day, if during the whole trip they walked 90 kilometres?

20km

25km

30km

40km

20 km or 30 km

None of the above answers is correct

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The students from some school got this problem as a homework: "Do there exist 5 integer numbers such that the sum of any two of them is smaller than 10, but the sum of any three of them is bigger than 10?". Which of the following is a full correct solution to this problem?

"No, there are no such numbers."

"Yes, there are such numbers."

"Answer: No. Explanation: If the sum of any two of the number is less than 10, then adding a very small of the numbers won't change the situation. So there will be three numbers such that their sum is also less than 10."

"Answer: Yes. Explanation: The sum of two numbers is less than the sum of three numbers. So we can make numbers of medium size and then everything will be okay, because all we need is sum of any two numbers is less than the sum of any three numbers."

None of the above can actually count as a full solution

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Please look at "For beginners" courses first, namely the "Getting started" course. Here is the link.

Please look at "For beginners" courses first, namely "Getting started" course. Here is the link.

Please look at "For beginners" courses first. Here is the link.

The results suggest that before you move on to "Olympiad Mathematics Training" you need to work on a few things like "what a proof is", "counterexamples", "logical puzzles". This is what "For beginners" courses are about. They are not hard, but extremely important. There are just two courses, pick one you think is more suitable for you.

If you think that you made some silly mistakes in this quiz, then you can try the next quiz and see what it says (but note that it is harder).

Please look at "For beginners" courses first, namely "Constructions, proofs a few nice ideas" course. Here is the link.

The results suggest that before you move on to "Olympiad Mathematics Training" you need to work a bit more on a few things like "formal proofs", "counterexamples", "formal logic". This is what "For beginners" courses are about. They are not hard, but extremely important. In your case, we would suggest doing the "Constructions, proofs a few nice ideas" course.

If you think that you made some silly mistakes in this quiz, then you can try the next quiz and see what it says (but note that it is harder).

Let's move on to the harder quiz! Click here.

You got all of the questions but one right, congratulations! This means that we should move on to the harder quiz now...

Let's move on to the harder quiz! Click here.

You got all of the questions right, congratulations! This means that we should move on to the harder quiz now...