Math Olympiad Grade5_03 on Day:.........Month:..........Year:...........

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Question 1: To complete the grid below, each of the digits from 1 to 4 must occur exactly once in each row and in each column. What number should replace X?.

Question 2: Ali is making squares using matches. He made the next square by adding more matches to the previous square as shown in the picture below.
How many matches does he have to add to the 5th square to build the 6th square?

Question 3: There were 60 birds on three trees. Then 6 birds flew away from the first tree, 8 birds flew away from the second tree and 4 birds flew away from the third tree.
Now there are the same number of birds on each tree. How many birds were there on the second tree in the beginning?

Question 4: The brothers Tom and Jason gave truthful answers to the question about the number of members their chess club has.
Tom said: “All the members of our club, except five girls, are boys.” Jason said: “Every six members always includes at least four girls.” What is the least number of members in their chess club?

Question 5: In the diagram below, the big square is divided into 7 identical squares and 2 identical triangles. The area of the shaded small square is 4 cm2. What is the total area of the shaded parts in cm2?

Question 6: A group of boys were picking apples. They each picked 3 apples. Then three other boys joined them. They wanted to share the picked apples equally among all the boys present, but found out that this was not possible.
However, one of the boys picked one more apple. Now everyone could have exactly two apples. How many boys were there in the original group?

Question 7: Let the operation ∗ be defined by 𝑎∗𝑏=𝑎𝑏−𝑎−𝑏+2. If 7∗𝑏=13, what is the value of b?

Question 8: A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces.
7 white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?

Question 9: Nora cut a grey shape from a square paper that is 6 cm by 6 cm.
Two vertices of the grey shape are the midpoints of the square's sides, and the other vertex is in the centre of the square. What is the area of the grey shape?

Question 10: A regiment has less than 1000 soldiers. The colonel planned in arranging the soldiers in the form of a rectangle. When he placed 17 soldiers in each row, one row was short of 1 soldier.
When he placed 13 soldiers in each row, one soldier remains. If the regiment consists of three "battalions", each with the same number of soldiers, how big is a "battalion"?