3rd and 4th grade, February, 2018

    A.1177. Olga noticed in a store that the numbers on the price tags are each a 3-digit number that is one less than the number rounded to the nearest tens, and if you round the prices to the nearest hundreds you always get 20 less than the number rounded to the nearest tens. Find all these 3-digit numbers.

    A.1178. You can see 9 little cars in the window of a toy store. From left to right every car (except for the first one) costs $2 more than the previous one. You can buy the one in the middle and the one on its left for the price of the last one all the way to the right. What are the prices of the least and the most expensive cars if you can buy all 9 of them for $90?

    A.1179. The Action Hero characters are very popular at the toy store. This week on Monday people already bought half of the inventory plus 4. By Wednesday 1/3 of the rest was sold, and only 46 of them were left in the inventory. How many Action Heroes were sold in the 3 days (from Monday to Wednesday)?

    A.1180. The third and fourth graders are going on a field trip to see a forest. On Monday the students went with the hunters to fill up the animal feeders. The deer feeder was 480 meters from the rabbit feeder, 60 meters farther than it is from the boar feeder. How far could the rabbit feeder be from the boar feeder if they are as far from each other as possible?

    A.1181. On Tuesday morning the students had three options: they could either go on a bird watch or on an insect watch tour, or they could stay back to do pottery. Three times as many (28 more) students chose to go on the bird watch than on the insect watch tour, and 12 students stayed for pottery. How many students are there on the trip? How many of them went on the bird watch and how many of them went on the insect watch tour?

    A.1182. On Tuesday afternoon the students played a game of “The War of the Numbered Kids.” In this game (3rd grade vs. 4th grade) each student places a card, with a 4-digit number on it, on his/her forehead. (The 3rd graders use red numbers and the 4th graders use blue numbers.) A student is out of the game if his/her number and the color of his/her number is read properly by somebody from the other team. The reader also has to describe the location of that student. Just calling out numbers randomly disqualifies you from the game. Students could pick a number below 2000, with a 1 or 7 on the tens place and an even digit on the hundreds place. The digit in the ones place cannot be less than 6. Each student on each team had to have a different number. How many students could participate on each team?

    A.1183. On Wednesday afternoon the students made bread. For one loaf of bread you need: 500 g of white flour, 500 g of rye flour, 20 g of yeast, 100 g of margarine, 50 g of sugar, 10 g of salt, 100 g of boiled potatoes, and 100 g of milk. The dough loses one tenth of its mass during baking. How much is the mass of one loaf of bread?

    A.1184. On Thursday the Fourth Grade organized a competition on an obstacle course in the forest. The 3-person teams left the hunters’ house every 8 minutes, and after a 40-minute tour they returned back there. What time did the last (the 16th) team get back to the house if the first team left at 8:45 am?

    Please send your solutions here.

    The Sharma Kamala Educational Trust is sponsoring the participation of students from India. So, if you are a student living in India, please, send your solutions to: Group A from India

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