Round 1 - Innovents Intermediate Math Quiz

Which of these is the sum of the cubes of two consecutive integers?

• 4

• 5

• 9

• 13

A kite is made by joining two congruent isosceles triangles, as shown. What is the value of x?

• 36

• 54

• 60

• 72

• 80

The adult human body has 206 bones. Each foot has 26 bones. Approximately what fraction of the number of bones in the human body is found in one foot?

• $\frac{1}{10}$

• $\frac{1}{20}$

• $\frac{1}{12}$

• $\frac{1}{8}$

• $\frac{1}{6}$

Which integer n satisfies

 $\frac{3}{10}<\frac{n}{20}<\frac{2}{5}$  ?

• 7

• 6

• 5

• 4

• 3

The three rectangles shown below all have the same area.

What is the value of x+y?

• 12

• 10

• 8

• 6

• 4

How many of these four integers are prime?

1 11 111 1111

• 0

• 1

• 2

• 3

• 4

In 2014, in Boston, Massachusetts, Eli Bishop set a world record for the greatest number of claps per minute. He achieved 1020 claps in one minute. How many claps is that per second?

• 17

• 16.5

• 16

• 15.5

• 15

What is 25% of three-quarters?

• 3

• 1

•  $\frac{1}{3}$  

•  $\frac{1}{4}$  

•  $\frac{3}{16}$  

An equilateral triangle is placed inside a larger equilateral triangle so that the diagram has three lines of symmetry. What is the value of x?

• 100

• 110

• 120

• 130

• 150

The shape shown was assembled from three identical copies of one of the smaller shapes below, without gaps or overlaps. Which smaller shape was used?

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