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Math Olympiad Group Problems

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Page 1: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

Math Olympiad Group Problems

Page 2: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of the larger square. What is the area of the smaller square?

Page 3: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

50 square meters

Page 4: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

What’s the missing number?

Page 5: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

39

Page 6: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

Solve the riddle:

I am a 2-digit prime number

I am greater than 20 and less than 60

The sum of my digits is 10

Who am I?

Page 7: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

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Page 8: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

Greg tosses 4 coins in the air and they come up 3 heads and 1 tail. Express the probability of this happening as a reduced fraction.

Page 9: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

¼

Page 10: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

One angle of a triangle has a measurement of 70 degrees. The ratio of the other two angles of the triangle is 5:6. What are the measurements of the other two angles?

Page 11: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

50 and 60 degrees

Page 12: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

King Kong climbed to the top of the 1250 foot tall Empire State Building. He would climb 150 feet, but then slip down 25 feet.

How many feet total did King Kong climb up during his journey to get to the top?

Page 13: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

1475 feet

Page 14: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

The odometer on a car reads 42322 km. In the next 200 km how often will the odometer show a number in which exactly three of the digits are the same?

Page 15: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

22

Page 16: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

A set of 5 whole numbers all more than 0 but less than 10 has a mean of 5, a mode of 2, and a median less than the mean. What is the set of numbers?

Page 17: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

{2, 2, 4, 8, 9}

Page 18: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

A group of scientists is duplicating cells for a science experiment. They observe that during each 10-minute period, one-quarter of the cells present died and the rest of the cells all doubled. If there were 32 cells initially, how many cells were there after 40 minutes?

Page 19: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

162 cells

Page 20: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

How many integers satisfy:

(n – 4)(n + 6) < 0?

Page 21: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

9

Page 22: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

A baseball team won 20% of its games and lost 12 games. How many games did the team play?

Page 23: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

15

Page 24: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

The sum of the areas of the two congruent circles shown is 72ft.2. What is the area of rectangle ABCD?

Page 25: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

288 sq. ft

Page 26: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

Square ABCD has a perimeter of 20 centimeters. If a circle is inscribed in the square, as shown, what is the area of the circle?

Page 27: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

or 19.625

26.25 cm2cm

Page 28: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

In an Olympic event, the winner of a triathlon swam 1 hour 42 minutes, then biked for 6 hours 59 minutes, then ran for 6 hours 13 minutes. If he started at 9:00 a.m., when did he finish?

Page 29: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

11:54 p.m.

Page 30: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

A genius reads 100 words backwards per second. How long does it take her to read 31,000 words backward?

Page 31: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

5 minutes and 10 seconds

Page 32: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

If each small circle has a diameter of 6 cm, and if the two small circles touch at the center of the large circle, what is the area of the shaded region?

Page 33: Math Olympiad Group Problems. The large square has an area of 100 square meters. The vertices of the other square lie at the midpoints of the sides of

or56.55

218 cm

2cm

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