High School (easy)

Challenge 19 – Straight line

How much is the area of the triangle formed by the lines whose equations are y = x, y =-x and y = 6?

Challenge 18 – Perimeter

In the diagram the BC segment connecting the centers of the circles. AB is perpendicular to BC, BC = AC = 8 and 10. The perimeter of the small circle is:

Challenge 17 – Equilateral triangle

An equilateral triangle DEF is equilateral enrolled in another ABC as shown in the figure, with DE perpendicular to BC. The ratio of the areas of triangles ABC and DEF is:

Challenge 15 – abc

If a, b and c are positive integers such that ac = b, bc = 12 and b = 3c, how much is abc?

Challenge 14 – Obtuse triangle

The sides of a triangle have lengths 11, 15 k, where k is an integer. For how many values of k the triangle is obtuse?

Challenge 13 – Number twenty

How many ways are there to write the number 20 as the exact sum of three prime numbers? (We do not consider 1 a primer number).

Challenge 12 – Three-digit

If X, Y and Z are different digits, then the largest possible amount that results in three digits has the form:

XXX

  YX

+ X
_____

a) XXY

b) XYZ

c) YYX

d) YYZ

Challenge 11 – Chewing gum

A gumball machine has 9 red gumballs, 7 white and 8 green. What is the smallest number of gumballs that you have to buy to make sure that you have 4 gumballs of the same color?

Challenge 10 – Baseball

One hundred persons went to baseball camp. Of these, 52 were right-handed and 48 left-handed, 40 were from the minor leagues of North and 60 South league. Twenty lefties were Northern League. How many right-handed persons were in the league the South league?

Challenge 9 – Positive values

How many positive values of n (n> 0) is the expression 36 / (n +2)  an integer?

Challenge  8 – Digit

What is the units digit of a product of six consecutive integers?

Challenge  7  – w, x, y, z

If w, x, y, z are four distinct digits of the set {1,2,3,4,5,6,7,8,9} and the sum w / x + y / z is as small as possible so   w / x + y / z equals how much?

Challenge 6 – Break the code

It is known that number A77C  is divisible by 12. If A and C are different A + C may be:

a)3

b)2

c)7

d)8

Challenge 5 – Zeros

How many zeros are at the end of the result of the multiplication of  24⁴ · 75³ · 15⁵ ?

Challenge 4 – Average

After 4 exams my average is 5. For my average to go up a point, how much should I score in the next test?

Challenge 3 – Sheet of paper

If you look at the physical challenges, you will meet a challenge (the number two) to measure the thickness of a sheet of paper. You can do it with the results you’ve obtained, or with the figures we present here:

Suppose you have a sheet that measures 30cm wide, 30cm long and has a thickness of 0.08mm. Now fold the sheet in half. It will look a sheet but half wide. Fold it again in half, it will be a square, but 15 cm from one side. Fold it in half once more, and then again … How many times can you fold the sheet?

Challenge 2 – A small calculation.

If you add to the numerator and denominator of 3/7 are the same number, you get 3/5. What is the number that is added?

Challenge 1 – Think and choose

Which of the following statements is true?

(a) (c) and (d) are not true. (b) (a) is false and (d) is true. (c) (a) is false (d) (a) is true, but not (c).