Grade 7J - Mommy at school competition

Mary numbered the sides of three cards from 1 to 6. Using these cards, she can compose three digit numbers, for example 135 or 234. But some numbers cannot be obtained, like 126. Which of the following numbers CANNOT be obtained?

• 134

• 146

• 235

• 245

Beatriz has six sisters with ages of 2, 3, 5, 8, 10 and 17. Beatriz writes these ages in the circles of the opposite diagram, so that the sum of the ages in the four corners of the square is equal to the sum of the ages in the four circles aligned horizontally.

What is this sum?

• 13

• 17

• 26

• 32

Inside the gray square there are three white squares and the numbers inside them indicate their areas. The white squares have sides parallel to the sides of the gray square. If the area of the gray square is 81, what is the area of the gray area not covered by the white squares?

• 25

• 43

• 52

• 68

Ten people order an ice cream for each one. They ask for four vanilla ice creams, three chocolate ice creams, two lemon ice creams and one mango ice cream. As a topping, they ask for four umbrellas, three cherries, two wafers and a chocolate gum, one topping for each ice cream. Since they don't want two ice creams the same, which of the following combinations is possible?

• Chocolat and chocolate gum.

• Mango and cherry.

• Lemmon and wafer.

• Lemmon and cherry.

A panel is composed of 4 circles. When Lucy touches a circle, this circle and the others that touch this circle change their color from white to black or from black to white, as shown in the picture. Starting with all white circles, at least how many circles must Lucy touch, one after the other, so that all circles turn black?

• 2

• 3

• 4

• 5

Carin is going to paint the walls in her room green. The green paint is too dark, so she mixes it with white paint. She tries different mixtures. Which of the following mixtures will give the darkest green colour?

• 1 part green + 3 parts white

• 2 parts green + 6 parts white

• 3 parts green+ 9 parts white

• They will all be equally dark

The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?

• 3

• 4

• 5

• 6

Three pirates were asked how many coins and how many diamonds their friend Graybeard had. Each of the three told the truth to one question but told a lie to the other. Their answers are written on the piece of paper pictured. What is the total number of coins and diamonds that Graybeard has?

• 12

• 13

• 14

• 15

My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CANNOT be the correct combination of my brother's lock?

• 
• 
• 
• 

When the 5 pieces are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?

• 22

• 32

• 41

• 122