G6 Math Olympiad Part F

Ike and Mike go into a sandwich shop with a total of $30 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

• 6

• 7

• 8

• 9

• 10

Three identical rectangles are put together to form rectangle ABCD , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?

• 45

• 75

• 100

• 125

• 150

Tags

CCSS.6.G.A.1

Tags

CCSS.4.NF.A.2

Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC is 24 meters. What is the area in square meters of rhombus ABCD?

• 60

• 90

• 105

• 120

• 144

Tags

CCSS.6.G.A.1

A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance d traveled by the two animals over time t from start to finish?

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Tags

CCSS.8.EE.B.5

There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that point Q is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?

Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76, 94, and 87 . In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?

• 48

• 52

• 66

• 70

• 74

Tags

CCSS.7.EE.B.3

Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?

• 20

• 38

• 45

• 54

Tags

CCSS.7.EE.B.3

Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume of one of Alex's cans to the volume one of Felicia's cans?

• 1 : 4

• 1 : 2

• 1 : 1

• 2 : 1

• 4 : 1

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually 21 participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?

• The mean increases by 1 and the median does not change.

• The mean increases by 1 and the median increases by 1.

• The mean increases by 1 and the median increases by 5.

• The mean increases by 5 and the median increases by 1.

• The mean increases by 5 and the median increases by 5.