Quantitative Reasoning Test (Data Collection)

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Welcome to the quantitative reasoning test.

There are in total 16 questions, do your best.

From question 9 and on you must input a number only.

Usage of a dictionary is allowed.

The test is untimed.

How old are you?
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What did you score on SB5, WAIS-IV etc.?

(Format the scores nicely; also subtest breakdown is preferred.)

Francisca has a square piece of paper whose sides have length 10 cm. She also has a rectangular piece of paper having the exact same area as the square piece of paper. She puts the rectangle right on top of the square, putting the left bottom corner of both pieces of paper in the same spot. Exactly one quarter of the square remains uncovered by the rectangle.

What is the length in centimetres of the long side of the rectangle?

1 point

12¼

12½

12¾

13⅓

Clear selection

A box measuring 4 dm by 15 dm is shoved against the wall. On top of it, a second box, measuring 12 dm by 6 dm, is placed. A ladder exactly touches the ground, the two boxes and the wall. See the figure (which is not drawn

to scale).

What is the length of the ladder in dm?

1 point

8√15

22√2

18√3

Clear selection

3. How many triangles are there in the figure?

1 point

Clear selection

In each square of the top three rows in the pyramid on the right, the number written in that square equals the sum of the numbers in the two squares below it. For three of the squares, the numbers written in them are given.

What number must be written in the square with the x in it?

1 point

Clear selection

A box contains red, white and blue balls. The number of red balls is an even number and the total number of balls in the box is less than 100. The number of white and blue balls together is 4 times as much as the number of red balls. The number of red and blue balls together is 6 times as much as the number of white balls.

How many balls are in the box?

1 point

Clear selection

Nine people are at a party. While entering, some of them shook hands. Quintijn is at the party

and asks each of the others how many hands they shook. He gets eight different answers.

How many hands did Quintijn shake?

1 point

Clear selection

For three distinct positive integers a, b, and c we have

a + 2b + 3c < 12.

Which of the following inequalities is certainly satisfied?

1 point

3a + 2b + c < 17

a + b + c < 7

a − b + c < 4

b + c − a < 3

3b + 3c − a < 6

Clear selection

A motorboat is moving with a speed of 25 kilometres per hour, relative to the water. It is going from New York to New Jersey, moving with the constant current. At a certain moment, it has travelled 42% of the total distance. From that point on, it takes the same amount of time to reach New York as it would to travel back to New Jersey.

What is the speed of the current (in kilometres per hour)?

1 point

Clear selection

Three years ago, Rosa’s mother was exactly five times as old as Rosa was at that time. At that moment, Rosa’s mother was just as old as Rosa’s grandmother was when Rosa’s mother was born. Now, Rosa’s grandmother is exactly seven times as old as Rosa is.

How old is Rosa’s mother now?

1 point

10.

Every day, Maurits bikes to school. He can choose between two different routes. Route B is 1.5 km longer than route A. However, because he encounters fewer traffic lights, his average speed along route B is 2 km/h higher than along route A. This makes that travelling along the two routes takes exactly the same amount of time.

How long does it take for Maurits to bike to school?

1 point

11.

Alice has a number of cards. Each card contains three of the letters A to I. For any choice of two of those letters, there is at least one card that contains both letters.

What is the smallest number of cards that Alice can have?

1 point

12.

A bus calls at three stops. The middle bus stop is equally far from the first stop as from the last stop. Fred, standing at the middle bus stop, has to wait for 15 minutes for the bus to arrive. If he cycles to the first stop, he will arrive there at the same time as the bus. If instead he runs to the last stop, he will also arrive there at the same moment as the bus.

How long would it take Fred to cycle to the last stop and then run back to the middle stop?

1 point

13.

An escalator goes up from the first to the second floor of a department store. Dion, while going up the escalator, also walks at a constant pace. Raymond, going in the opposite direction, tries to walk downwards, from the second to the first floor, on the same escalator. He walks at the same pace as Dion. They both take one step of the escalator at a time. Dion arrives at the second floor after exactly 12 steps; Raymond arives at the first floor after exactly 60 steps.

How many steps would it take Dion to get upstairs if the escalator would stand still?

1 point

14.

Annemiek and Bart each have a note on which they have written three different positive integers. It appears that there is exactly one number that is on both their notes. Moreover, if you add any two different numbers from Annemiek’s note, you get one of the numbers on Bart’s note. One of the numbers on Annemiek’s note is her favourite number, and if you multiply it by 3, you get one of the numbers on Bart’s note. Bart’s note contains the number 25, his favourite number.

What is Annemiek’s favourite number?

1 point

15.

We call a positive integer sunny if it has four digits and if moreover each of the two digits on the outside is exactly 1 larger than the digit next to it. The numbers 8723 and 1001 for example are sunny, but 1234 and 87245 are not.

How many sunny numbers are there such that twice the number is again a sunny number?

1 point

16.

The eight points below are the vertices and the midpoints of the sides of a square. We would like to draw a number of circles through the points, in such a way that each pair of points lie on (at least) one of the circles.

Determine the smallest number of circles needed to do this.

1 point

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