Math reasoning

A

100

A person walks:

• 4 meters north,
• 3 meters east,
• 4 meters south.

Where is the person relative to the starting point?

3 meters east

200

Five years ago, Maria was three times as old as her brother. In five years, she will be twice as old as him.

How old is Maria now?

She is 35 years old.

300

What is the missing number?

3, 8, 18, 38, 78, ___

158

400

Five students — Ana, Ben, Carla, David, and Emma — are standing in a line.

• Ana is immediately to the left of Ben.
• Carla is at one end of the line.
• Emma is not next to Carla.
• David is between Ben and Emma.

Who is in the middle?

Ben is in the middle.

500

If

a−b=4  and ab=12. Find the value of a² + b²

40

B

100

A cube has the numbers 1 through 6 on its faces. If face 1 is opposite face 6 and face 2 is opposite face 5, which face is opposite face 3?

face 4

200

A father is currently four times as old as his son. In 12 years, the father will be twice as old as his son.

How old is the son now?

The son is 6 years old.

300

Find the next number.

2, 3, 5, 9, 17, 33, ___

65

400

Four friends — Lucas, Maria, Pedro, and Sofia — sit around a square table.

• Lucas sits opposite Sofia.
• Maria sits to the right of Lucas.

Who sits opposite Maria?

Pedro sits opposite Maria.

500

A number is increased by 5 and the result is multiplied by 3. This value is equal to twice the number increased by 20.

What is the number?

5

C

100

A sheet of paper is folded in half twice and then a hole is punched through the folded paper. When the paper is completely unfolded, how many holes will appear?

4 holes

200

The sum of a mother’s and daughter’s ages is 60. Ten years ago, the mother was three times as old as her daughter.

How old is the daughter now?

She is 15 years old.

300

Find the missing number.

1, 2, 6, 24, 120, ___

720

400

Five books are placed on a shelf.

• The History book is to the left of the Science book.
• The Math book is between the Science and English books.
• The English book is at the far right.
• The Art book is at the far left.

Which book is in the middle?

The Science book is in the middle.

500

If

x+y=10  and xy=21, what is the value of x² +y²

58

D

100

A cube is painted red on all six faces and then cut into 64 smaller cubes of equal size.

How many small cubes have exactly three painted faces?

8 small cubes

200

John is twice as old as Peter. Eight years ago, John was three times as old as Peter.

How old is Peter now?

Peter is 16 years old now.

300

1, 1, 2, 3, 5, 8, 13, 21, ___

34

400

Five runners finish a race.

• Alex finishes before Brian.
• Brian finishes before Carlos.
• Diana finishes after Carlos.
• Ethan finishes before Alex.

Who finishes third?

Brian finishes third.

500

Four students — Laura, Miguel, Natalia, and Oscar — each play a different musical instrument (Piano, Guitar, Violin, Drums) and would like to visit a different country (Japan, Canada, Brazil, Italy).

Clues

1. The student who plays the Violin wants to visit Italy.
2. Miguel does not play the Guitar or the Drums.
3. Laura wants to visit Canada.
4. Oscar does not want to visit Italy.
5. Natalia plays the Drums.
6. The student who wants to visit Japan plays the Piano.
7. Miguel wants to visit Italy.

    Which instrument does Miguel play? 

Miguel plays the violin.

E

100

A cube is placed on a table. The face on top shows 5, the face facing you shows 2, and the face on the right shows 3.

The cube is rotated so that the face showing 2 moves to the top. Which face will now be facing you?

face 5

200

Three years ago, Ana was twice as old as Luis. Six years from now, the sum of their ages will be 48.

How old is Ana now?

Ana is 23 years old.

300

Find the missing number in the sequence:

4, 7, 13, 25, 49, ___

97

400

Five houses are painted different colors: Red, Blue, Green, Yellow, and White.

• The Green house is immediately to the right of the Blue house.
• The Red house is at one end.
• The White house is not next to the Red house.
• The Yellow house is between the Green and White houses.

Which color is the house in the middle?

It´s green.

500

A cube has six faces labeled A, B, C, D, E, and F.

• Face A is opposite F.
• Face B is opposite E.
• Face C is opposite D.

The cube is placed on a table with:

• A on the top,
• B on the front,
• C on the right.

The cube is then rotated so that the front face (B) moves to the top.

Which face will now be on the front?

Face F