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for 5th and 6th graders

January, 2013

B.889. Anton and Ben are competing in 50-meter speed walking. They each walk

with a constant speed for the whole race. If they start at the same point at the

same time, Anton beats Ben by 10 meters at the finish line. So now Anton start

from 10 meters behind the starting line giving Ben a handicap. If they start at

the same time, and they both walk by the same speed as they did in the previous

race, who wins the race this time and by how much distance?

B.890. A spiral is given with its center point X. As you walk on the spiral, you

continually get farther away from its center point. The spiral never ends. The

picture shows only the beginning of it. Now you draw a circle with the same

center point. How many mutual points do the two curves have?

B.891. You have two circular discs with a radius of 9 cm each. You want to covera 10-cm radius circular disc with them completely. How many different ways

can you do it?

B.892. Tom's father loves chocolate balls. You can buy them in 3 different bags:

one contains 6, the other contains 9, and the third kind contains 20 chocolate

balls. You may not open the bags before you buy them. Tom wants to surprise

his father on his birthday by buying as many chocolate balls as many years old

his father is. Unfortunately, Tom cannot do it this year, but starting next year he

will be able to do it every year. How old is Tom's father this year?

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Math Teacher: DANG Minh Tuan
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B.893. Out of 40 shoppers, 12 of them liked the apples, 23 liked the oranges, and

twice as many did not like either as many liked both. How many shoppers liked

both?

B.894. If you read a two-digit number backwards, you get a 4.5 times greater

number. Find this number.

B.895. In a group of people the ratio of the number of women and the number of

men is 11:10. The average age of the women is 34, and the average age of the

men is 32. What is the average age of the group exactly?

B.896. You have a lot of 1 cubic centimeter volume cubes. Build a column with a

2cm x 2cm base. How tall is the column if its surface area is 2000 square

centimeters?

for7th and 8th gradersJanuary, 2013

C.889. Find the prime numbers a, b, c, and d, if a + b = c, and a - b = d. (a minus

b = d)

C.890. A 182 cm tall man is digging a hole in the ground. He stops for a moment

and says: "I am done with one quarter of the hole. When I finish the job the top

of my head is going to be three times as far under the ground as far it is above

the ground now." How deep is the hole going to be?

C.891. A man leaves his house in the morning at the same time every day. He

rides his bicycle to work along the train tracks with a speed of 12 km/h, so he

arrives to a railroad crossing every day at the same time as the train going in the

same direction as he does. The train always goes by the same speed and is always

on schedule. One morning the man did not wake up on time, and left his house

50 minutes late. Therefore, he met the train 12 km before the railroad crossing.

How much longer does it take the train to get to the railroad crossing?



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C.892. There are 8 identical boxes in which there are 1, 2, 4, 8, ..., 128 pearls, but

we do not know which box has how many pearls in it. Cecilia picks a few of the

boxes, and gives the rest of the boxes to Mary. When they both opened their

boxes, it turned out that Cecilia received 31 more pearls than Mary. How manyboxes did Cecilia choose, and how many pearls were in them each?

C.893. Two wine merchants are going into town to sell their wine. At the gate

they have to pay taxes based on the value of the wine they want to take into the

town. The first merchant has 64 barrels of wine and he has to pay 5 barrels of

wine and 40 golden coins. The other merchant has 20 barrels of wine (the same

kind of barrels and the same wine), and he gives 2 barrels of wine but gets back

40 golden coins. How many golden coins is the price of a barrel of wine, and howmuch is the tax on it?

C.894. You have 12 one-unit-long straight segments. Using them, create a

polygon with an area of 3 units.

C.895. We cut up a rectangle into 9 square-shaped pieces with sides 1, 4, 7, 8, 9,

10, 14, 15, and 18 units. (Every square is in one piece, so we cut up the rectangle

into 9 pieces.) How long were the sides of the rectangle if you know that they are

whole numbers?

C.896. We extended the BC side of the equilateral triangle, ABC, by the half of

the side over C to get point D. The straight segment, starting from point D, going

through the midpoint F of side AC, intersects side AB in point E. What part of

the perimeter of ABC is the length of segment AE?

Note: Students should do all problems above as much as possible!



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tth_aba_jan13_hw17

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