G6 Math Olympiad Part D

Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. In the end, he has 10 pieces of pasta whose total length is 17 inches. How long, in inches, was the piece of pasta he started with?

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Tags

CCSS.4.MD.A.2

The arrows on the two spinners shown below are spun. Let the number N equal 10 times the number on Spinner A, added to the number on Spinner B. What is the probability that is a perfect square number?

How many positive integers can fill the blank in the sentence below?

“One positive integer is _____ more than twice another, and the sum of the two numbers is 28.”

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• 10

Tags

CCSS.7.EE.B.3

In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?

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• 120

Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?

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Tags

CCSS.7.RP.A.2C

Four numbers are written in a row. The average of the first two is 21，the average of the middle two is 26，and the average of the last two is 30. What is the average of the first and last of the numbers?

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• 28

Tags

CCSS.7.EE.B.3

If n is an even positive integer, the double factorial notation n!! represents the product of all the even integers from 2 to n. For example, 8!!=2・4・6・8. What is the digit on ones place of the following sum?

2!! + 4!! + 6!! +....+ 2018!! + 2020!! +2022!!

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Tags

CCSS.HSF.BF.A.2

The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4) and (0,4). What is the area of the rectangle?

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Tags

CCSS.6.G.A.3

Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores.

Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students extra 5 points, which increased the median test score to 85. What is the minimum number of students who received extra points?

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The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number X in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of X?

• -1

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Tags

CCSS.8.EE.C.7B