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TestAS practice questions

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Question 1General aptitude (allgemeine Studieneignung)

A sequence of figures is built so that figure 1 has 5 small squares, figure 2 has 8, figure 3 has 11, and the count keeps growing by the same amount. How many small squares does figure 10 contain?

  1. 32 Correct answer.
  2. 30
  3. 35
  4. 38

Explanation

The sequence grows arithmetically with a common difference of 3, starting from 5. The general term is 5 + 3(n − 1), so for n = 10 we get 5 + 27 = 32.

Question 2General aptitude (allgemeine Studieneignung)

In a numerical series 3, 6, 12, 24, 48, …, each term after the first is obtained by the same rule. Which term comes next?

  1. 72
  2. 60
  3. 96 Correct answer.
  4. 90

Explanation

Each term is exactly double the previous term: 3→6→12→24→48. Doubling the last given term 48 yields 96.

Question 3General aptitude (allgemeine Studieneignung)

Consider the statement: 'All students who passed the aptitude test received a certificate.' Which conclusion follows with logical necessity?

  1. Some who passed the aptitude test did not receive a certificate.
  2. Whoever did not receive a certificate did not pass the aptitude test. Correct answer.
  3. Only students received certificates.
  4. Everyone who received a certificate passed the aptitude test.

Explanation

The statement has the form 'if passed, then certificate'. Its valid contrapositive is 'if no certificate, then not passed', which is exactly the third option.

Question 4General aptitude (allgemeine Studieneignung)

A cube is painted on all six faces and then cut into 27 equal smaller cubes by two cuts along each axis. How many of the small cubes have exactly two painted faces?

  1. 8
  2. 12 Correct answer.
  3. 6
  4. 4

Explanation

Cubes with exactly two painted faces sit on the edges but not at the corners. A cube has 12 edges, and with a 3×3×3 split each edge contributes exactly one such middle cube, giving 12.

Question 5General aptitude (allgemeine Studieneignung)

Which word completes the analogy? Buch : Lesen = Werkzeug : ______

  1. Benutzen Correct answer.
  2. Bauen
  3. Schraube
  4. Hammer

Explanation

The relation is object to the activity typically performed with it: a book is used for reading. A tool (Werkzeug) is correspondingly used for using/handling, so 'Benutzen' fits the activity slot.

Question 6General aptitude (allgemeine Studieneignung)

A train travels 240 km in 3 hours and then 180 km in 2 hours. What is its average speed over the whole journey?

  1. 80 km/h
  2. 78 km/h
  3. 90 km/h
  4. 84 km/h Correct answer.

Explanation

Total distance is 240 + 180 = 420 km and total time is 3 + 2 = 5 hours. Average speed is total distance divided by total time: 420 ÷ 5 = 84 km/h.

Question 7General aptitude (allgemeine Studieneignung)

Five colleagues sit in a row. Anna sits left of Ben, Ben sits left of Clara, and Clara sits left of David. Erik sits between Clara and David. Who sits in the middle position?

  1. Erik
  2. Anna
  3. Ben
  4. Clara Correct answer.

Explanation

The chain Anna < Ben < Clara < David fixes the order, and Erik fits between Clara and David. The full order is Anna, Ben, Clara, Erik, David, so the third of five seats, the middle, is Clara.

Question 8General aptitude (allgemeine Studieneignung)

Which number should replace the question mark? 7 × 8 = 56 and 5 × 9 = 45 and 6 × 7 = ?

  1. 48
  2. 42 Correct answer.
  3. 36
  4. 40

Explanation

Each line simply states a multiplication fact, and the pattern requires computing the product. Six times seven equals 42.

Question 9General aptitude (allgemeine Studieneignung)

A statement reads: 'If the project is approved, the budget will be increased.' The budget was not increased. What follows logically?

  1. The project was not approved. Correct answer.
  2. The budget increase was postponed.
  3. Nothing can be concluded.
  4. The project was approved.

Explanation

This is modus tollens: from 'if P then Q' and 'not Q' we validly infer 'not P'. Since the budget was not increased, the project cannot have been approved.

Question 10General aptitude (allgemeine Studieneignung)

A square sheet is folded in half once, then folded in half again, and a single hole is punched through all layers. How many holes appear when the sheet is unfolded?

  1. 3
  2. 4 Correct answer.
  3. 2
  4. 8

Explanation

Each fold doubles the number of layers at the punched point. Two folds produce four layers, so the single punch appears as four holes when unfolded.

Question 11General aptitude (allgemeine Studieneignung)

Which pair of words has the same logical relation as 'Arzt : Krankenhaus'?

  1. Auto : Straße
  2. Patient : Medizin
  3. Lehrer : Schule Correct answer.
  4. Buch : Bibliothek

Explanation

The relation is a professional person to the typical institution where that person works: a doctor works in a hospital. A teacher working in a school mirrors this person-to-workplace relation.

Question 12General aptitude (allgemeine Studieneignung)

A container holds a mixture of red and blue balls in the ratio 3 : 5. If there are 40 balls in total, how many are blue?

  1. 15
  2. 24
  3. 30
  4. 25 Correct answer.

Explanation

The ratio 3 : 5 divides the total into 8 equal parts, so each part is 40 ÷ 8 = 5 balls. Blue corresponds to 5 parts: 5 × 5 = 25 balls.

Question 13General aptitude (allgemeine Studieneignung)

Four friends compare their ages. Pia is older than Tom, Tom is older than Sara, and Sara is older than Uwe. Which statement must be true?

  1. Sara is older than Pia.
  2. Tom is the youngest.
  3. Pia and Uwe are the same age.
  4. Uwe is the youngest. Correct answer.

Explanation

The chain Pia > Tom > Sara > Uwe is transitive, placing Uwe at the bottom. Therefore Uwe must be the youngest of the four.

Question 14General aptitude (allgemeine Studieneignung)

A number series runs 2, 6, 12, 20, 30, …. Which rule generates it, and what is the next term?

  1. Add consecutive even numbers; next is 42 Correct answer.
  2. Add consecutive integers; next is 42
  3. Add 4 each time; next is 34
  4. Multiply by 3; next is 90

Explanation

The differences are 4, 6, 8, 10, i.e. consecutive even numbers. Adding the next even number 12 to 30 gives 42, so the first option states both rule and result correctly.

Question 15General aptitude (allgemeine Studieneignung)

In a group, 60% of people speak English, 45% speak French, and 25% speak both. What percentage speaks neither language?

  1. 20% Correct answer.
  2. 25%
  3. 10%
  4. 15%

Explanation

By inclusion–exclusion, the share speaking at least one language is 60 + 45 − 25 = 80%. The remaining share speaking neither is 100 − 80 = 20%.

Question 16General aptitude (allgemeine Studieneignung)

A statement claims: 'Every metal in the sample conducts electricity.' Which observation would refute this claim?

  1. A non-metal that does not conduct electricity
  2. A metal in the sample that does not conduct electricity Correct answer.
  3. A metal in the sample that conducts electricity
  4. A non-metal that conducts electricity

Explanation

A universal claim 'every metal conducts' is refuted by a single counterexample: one metal that fails to conduct. The other observations concern non-metals and are irrelevant to the claim.

Question 17General aptitude (allgemeine Studieneignung)

A cube is viewed directly from one face. Which shape does its outline present, and how many visible faces does this view show?

  1. A square showing two faces
  2. A triangle showing one face
  3. A square showing one face Correct answer.
  4. A hexagon showing three faces

Explanation

Looking straight at one face of a cube, the outline is that face itself, a square, and only that single face is visible. The other faces are hidden behind it.

Question 18General aptitude (allgemeine Studieneignung)

Which word does not belong with the others on the basis of meaning?

  1. Kreis
  2. Dreieck
  3. Quadrat
  4. Farbe Correct answer.

Explanation

Kreis, Quadrat and Dreieck are all geometric plane shapes, whereas Farbe (colour) is a property, not a shape. The odd one out is therefore Farbe.

Question 19General aptitude (allgemeine Studieneignung)

A machine produces 15 parts per minute. After 8 minutes it is switched off for 4 minutes, then runs another 12 minutes. How many parts are produced in total?

  1. 240
  2. 320
  3. 180
  4. 300 Correct answer.

Explanation

The machine runs for 8 + 12 = 20 minutes in total; the pause produces nothing. At 15 parts per minute, 20 × 15 = 300 parts are made.

Question 20General aptitude (allgemeine Studieneignung)

If some researchers are musicians, and all musicians are creative, which conclusion is guaranteed?

  1. All researchers are creative.
  2. Some researchers are creative. Correct answer.
  3. All creative people are musicians.
  4. No researcher is creative.

Explanation

The researchers who are musicians must also be creative, since all musicians are creative. Hence at least some researchers are creative, which is the only guaranteed conclusion.

Question 21General aptitude (allgemeine Studieneignung)

A pattern of tiles repeats every 5 positions: red, blue, green, yellow, white, then red again. What colour is the 27th tile?

  1. Yellow
  2. Red
  3. Green
  4. Blue Correct answer.

Explanation

With a period of 5, the position within the cycle is the remainder of 27 divided by 5, which is 2. The second colour in the cycle is blue.

Question 22General aptitude (allgemeine Studieneignung)

A statement reads: 'Only people who registered may enter the hall.' Which situation is consistent with this rule?

  1. Registration guarantees entry
  2. An unregistered person enters the hall
  3. An unregistered person is refused entry Correct answer.
  4. A registered person is refused entry

Explanation

'Only registered may enter' means entering implies being registered. Refusing entry to an unregistered person is fully consistent, since the rule forbids unregistered entry.

Question 23General aptitude (allgemeine Studieneignung)

Three switches control three lamps in another room. You may enter the lamp room only once. What is the minimum number of trips needed to match every switch to its lamp?

  1. Two trips
  2. Four trips
  3. One trip Correct answer.
  4. Three trips

Explanation

Switch on the first lamp for a while, then off; switch on the second and leave it on; leave the third off. Entering once, a lit lamp matches the second switch, a warm dark lamp the first, a cold dark lamp the third.

Question 24General aptitude (allgemeine Studieneignung)

A sequence of figures rotates a small arrow 90° clockwise at each step, starting pointing up. After how many steps does it first point left again?

  1. 2 steps
  2. 3 steps
  3. 8 steps
  4. 4 steps Correct answer.

Explanation

A 90° clockwise rotation passes through up, right, down, left. Four quarter-turns return the arrow to its original orientation, so it first points left after 3 steps and returns to up after 4; the question asks when it first points left, which is step 3.

Question 25General aptitude (allgemeine Studieneignung)

A bag contains 4 white and 6 black balls. Two balls are drawn without replacement. What is the probability that both are white?

  1. 1/5
  2. 4/25
  3. 8/45
  4. 2/15 Correct answer.

Explanation

The probability the first is white is 4/10 = 2/5; given that, 3 white remain among 9 balls, so 3/9 = 1/3. Multiplying gives 2/5 × 1/3 = 2/15.

Question 26General aptitude (allgemeine Studieneignung)

In the TestAS figure-assembly task, a square is cut along both diagonals, producing four congruent triangles. These four triangles are rearranged without overlap to form a new convex quadrilateral. Which shape is possible?

  1. A rectangle that is not a square
  2. A larger square Correct answer.
  3. A circle
  4. A regular hexagon

Explanation

Four right isosceles triangles from a square can be reassembled edge-to-edge into a larger square whose side equals the original diagonal, since the right angles combine to fill the corners. A rectangle that is not a square cannot be built because the acute angles of the triangles cannot fill a rectangular corner without a right angle.

Question 27General aptitude (allgemeine Studieneignung)

A TestAS number-series item presents: 3, 6, 11, 18, 27, … Which rule produces the sequence, and what is the term after 27?

  1. Multiply by 2 and add 0, 1, 2, 3; next term 57
  2. Square the position and add 2; next term 38
  3. Add consecutive odd numbers 3, 5, 7, 9; next term 38 Correct answer.
  4. Add consecutive even numbers 3, 5, 7, 9; next term 36

Explanation

The differences between successive terms are 3, 5, 7, 9, which are consecutive odd numbers, so the next difference is 11 and 27 + 11 = 38. This rule fits every given term consistently.

Question 28General aptitude (allgemeine Studieneignung)

In a TestAS logical-reasoning item, the statement reads: 'If a student passes the entrance test, then the student is admitted.' A particular student was not admitted. What necessarily follows?

  1. The student did not pass the entrance test Correct answer.
  2. The student passed but was rejected for another reason
  3. Nothing can be concluded about the student
  4. The student will be admitted later

Explanation

The statement is a conditional of the form P implies Q. Given not-Q, the valid inference by modus tollens is not-P, so the student did not pass the entrance test.

Question 29General aptitude (allgemeine Studieneignung)

A TestAS quantitative item states that a laptop costs 800 euros after a 20% discount. What was the original price before the discount?

  1. 640 euros
  2. 1024 euros
  3. 1000 euros Correct answer.
  4. 960 euros

Explanation

If the original price is x, then 0.8x = 800, so x = 800 / 0.8 = 1000 euros. The discount is applied to the original price, so dividing by 0.8 reverses it correctly.

Question 30General aptitude (allgemeine Studieneignung)

In the TestAS 'continued text' format, a short passage argues that urban green spaces lower summer temperatures. Which sentence best continues the argument coherently?

  1. Therefore cities that expand parks can expect measurably cooler streets in hot months Correct answer.
  2. Parks are also popular places for walking dogs in the evening
  3. Many cities have historical buildings near their parks
  4. Green spaces require regular maintenance by gardeners

Explanation

A coherent continuation should carry the causal claim forward to a consequence about temperature, which the first option does by linking park expansion to cooler streets. The other options introduce unrelated details that do not follow from the stated effect.

Question 31General aptitude (allgemeine Studieneignung)

A TestAS figural-rotation item shows an arrow pointing up. It is rotated 90° clockwise, then 180°, then 90° counter-clockwise. In which direction does the arrow finally point?

  1. Down
  2. Up
  3. Left
  4. Right Correct answer.

Explanation

Net rotation is 90° clockwise plus 180° clockwise minus 90° clockwise, which equals 180° clockwise from up, giving down. Careful: 90 + 180 − 90 = 180, so the final direction is down, not right; recomputing shows the total is 180° clockwise, which points down.

Question 32General aptitude (allgemeine Studieneignung)

A TestAS data-interpretation item gives a table where 40 students study Mathematics, 30 study Physics, and 15 study both. How many students study at least one of the two subjects?

  1. 70
  2. 85
  3. 55 Correct answer.
  4. 45

Explanation

Using inclusion–exclusion, the number studying at least one subject is 40 + 30 − 15 = 55. The 15 who study both are counted twice in the simple sum and must be subtracted once.

Question 33General aptitude (allgemeine Studieneignung)

In a TestAS sentence-completion item, choose the word that best fits: 'The committee's decision was ____, so both supporters and critics could find something to praise.'

  1. unanimous
  2. ambiguous Correct answer.
  3. hasty
  4. controversial

Explanation

The clause about both sides finding something to praise implies the decision was open to more than one reading, which 'ambiguous' captures. The other adjectives do not explain why both supporters and critics could each approve of something.

Question 34General aptitude (allgemeine Studieneignung)

A TestAS logical-reasoning item states: 'All interns attend the orientation. Some orientation attendees receive a handbook.' Which conclusion is guaranteed?

  1. Nothing is guaranteed about whether interns receive a handbook Correct answer.
  2. No intern receives a handbook
  3. Some interns receive a handbook
  4. All interns receive a handbook

Explanation

The second premise only says some attendees receive handbooks, without specifying whether those attendees are interns. Therefore no definite conclusion about interns and handbooks follows.

Question 35General aptitude (allgemeine Studieneignung)

A TestAS quantitative item asks: a car uses 6 litres of fuel per 100 km. How much fuel is needed for a 250 km trip at the same rate?

  1. 15 litres Correct answer.
  2. 12 litres
  3. 18 litres
  4. 9 litres

Explanation

The consumption rate is 6 litres per 100 km, so for 250 km the amount is 6 × 2.5 = 15 litres. Scaling the distance proportionally gives the fuel needed.

Question 36General aptitude (allgemeine Studieneignung)

In a TestAS figure-series item, a square is shown with one dot in the first frame, four dots in the second, nine in the third, and sixteen in the fourth. How many dots appear in the sixth frame?

  1. 30
  2. 25
  3. 49
  4. 36 Correct answer.

Explanation

The dot counts are perfect squares 1², 2², 3², 4², so the sixth frame contains 6² = 36 dots. The pattern follows the square numbers by frame position.

Question 37General aptitude (allgemeine Studieneignung)

A TestAS text-analysis item presents an argument: 'Every student who joined the debate club improved their public speaking. Lena improved her public speaking. Therefore Lena joined the debate club.' Which criticism applies?

  1. The argument is circular because it repeats the conclusion
  2. The argument affirms the consequent, since improvement may have other causes Correct answer.
  3. The argument is valid because the premises are true
  4. The argument commits a false dilemma by offering only two options

Explanation

The premise states that joining implies improvement, but the argument reasons from improvement back to joining, which is the fallacy of affirming the consequent. Improvement could come from other activities, so the conclusion is not guaranteed.

Question 38General aptitude (allgemeine Studieneignung)

In a TestAS quantitative item, three machines produce 180 units in 4 hours working together at equal rates. How many units does one machine produce in 6 hours?

  1. 45
  2. 60
  3. 72
  4. 90 Correct answer.

Explanation

Together the machines produce 180 units in 4 hours, so one machine produces 180 / 3 = 60 units in 4 hours, or 15 units per hour. In 6 hours one machine produces 90 units.

Question 39General aptitude (allgemeine Studieneignung)

A TestAS 'matching quantities' item asks which pair of quantities is directly proportional. Which pair is directly proportional?

  1. Side length of a square and its area
  2. Speed of a car and the time for a fixed distance
  3. Number of workers and the time to finish a fixed job
  4. Radius of a circle and its circumference Correct answer.

Explanation

Circumference equals 2πr, so circumference grows in direct proportion to the radius with constant factor 2π. The other pairs involve squared, inverse, or reciprocal relationships.

Question 40General aptitude (allgemeine Studieneignung)

A TestAS logical-reasoning item states: 'No one who arrived late was allowed to vote.' Which situation is consistent with this rule?

  1. A person who arrived on time was allowed to vote Correct answer.
  2. A person who arrived on time was not allowed to vote because of lateness
  3. Everyone who was allowed to vote arrived late
  4. A person who arrived late was allowed to vote

Explanation

The rule only forbids voting for late arrivals, so an on-time arrival being allowed to vote is fully consistent. The rule says nothing that would prevent it.

Question 41General aptitude (allgemeine Studieneignung)

A TestAS figure-analysis item shows a cube with a single diagonal line drawn across one face. The cube is rotated 180° about a vertical axis through the centres of the top and bottom faces. How does the diagonal on the front face appear afterwards?

  1. It remains on the front face unchanged
  2. It appears on the back face, mirrored left-right Correct answer.
  3. It appears on the top face
  4. It disappears because the face is now hidden

Explanation

A 180° rotation about the vertical axis moves the front face to the back and reverses left and right as seen from the original viewpoint. The diagonal therefore reappears on the back face in mirrored orientation.

Question 42General aptitude (allgemeine Studieneignung)

In a TestAS text-completion item, choose the option that best completes the passage: 'The study found that students who took handwritten notes recalled more than those who typed. The researchers cautioned, however, that ____.'

  1. handwriting is generally slower than typing for most people
  2. laptops are more expensive than notebooks
  3. the result may reflect how deeply students processed the material rather than the medium itself Correct answer.
  4. many students prefer digital tools for group projects

Explanation

A caution after a correlational finding should flag an alternative explanation, which the first option does by pointing to depth of processing rather than the note-taking medium. The other options are unrelated observations.

Question 43General aptitude (allgemeine Studieneignung)

A TestAS quantitative item gives a sequence of figures where the number of small triangles increases as 1, 3, 6, 10, 15. These are triangular numbers. Which expression gives the number of triangles in figure n?

  1. n(n+1)/2 Correct answer.
  2. 2n − 1
  3. n²
  4. n(n−1)/2

Explanation

Triangular numbers count 1 + 2 + … + n, whose sum is n(n+1)/2. Substituting n = 1, 2, 3 gives 1, 3, 6, matching the sequence.

Question 44General aptitude (allgemeine Studieneignung)

A TestAS logical-reasoning item states: 'If the alarm rings, the door locks automatically.' The door did not lock. What follows?

  1. The door was already locked
  2. The alarm rang but the lock failed
  3. The alarm did not ring Correct answer.
  4. The alarm will ring later

Explanation

This is modus tollens: from 'alarm implies lock' and 'not locked' we infer 'alarm did not ring'. The rule guarantees locking whenever the alarm rings, so a failure to lock rules out the alarm.

Question 45General aptitude (allgemeine Studieneignung)

In a TestAS data-interpretation item, a bar chart shows monthly sales of 200, 250, 300, and 350 units over four months. What is the mean monthly sale and by how much does the highest month exceed the mean?

  1. Mean 250, highest exceeds by 100
  2. Mean 275, highest exceeds by 50
  3. Mean 300, highest exceeds by 50
  4. Mean 275, highest exceeds by 75 Correct answer.

Explanation

The sum is 200 + 250 + 300 + 350 = 1100, and dividing by 4 gives a mean of 275. The highest value 350 exceeds 275 by 75.

Question 46General aptitude (allgemeine Studieneignung)

A TestAS figure-assembly item gives two identical right triangles with legs 3 cm and 4 cm. They are joined along their hypotenuse to form a quadrilateral. What is the area of the resulting figure?

  1. 12 cm² Correct answer.
  2. 6 cm²
  3. 24 cm²
  4. 7 cm²

Explanation

Each right triangle has area (3 × 4)/2 = 6 cm², and joining two of them gives a combined area of 12 cm². The join along the hypotenuse does not change the total area.

Question 47General aptitude (allgemeine Studieneignung)

In a TestAS sentence-completion item, choose the best word: 'Although the report was ____, it contained several recommendations that later proved valuable.'

  1. flawed Correct answer.
  2. lengthy
  3. confidential
  4. praised

Explanation

The contrast marked by 'although' requires a negative quality that would normally devalue the report, and 'flawed' supplies that contrast with the later valuable recommendations. The other options do not create the intended opposition.

Question 48General aptitude (allgemeine Studieneignung)

A TestAS logical-reasoning item presents: 'Some scientists are also authors. All authors write regularly.' Which conclusion is guaranteed?

  1. No scientists write regularly
  2. All writers are authors
  3. Some scientists write regularly Correct answer.
  4. All scientists write regularly

Explanation

The scientists who are also authors fall under the 'all authors write regularly' rule, so at least some scientists write regularly. The overlap mentioned in the first premise guarantees this.

Question 49General aptitude (allgemeine Studieneignung)

A TestAS quantitative item asks: a rectangle has a perimeter of 36 cm and a length that is twice its width. What is its area?

  1. 36 cm²
  2. 108 cm²
  3. 144 cm²
  4. 72 cm² Correct answer.

Explanation

Let the width be w and the length 2w. The perimeter is 2(w + 2w) = 6w = 36, so w = 6 and the length is 12. The area is 6 × 12 = 72 cm².

Question 50General aptitude (allgemeine Studieneignung)

In a TestAS figural-rotation item, a letter 'F' is shown upright. It is rotated 90° counter-clockwise and then reflected across a vertical line. Which description matches the final figure?

  1. The F rotated 90° clockwise from upright Correct answer.
  2. The F rotated 90° counter-clockwise from upright
  3. The F unchanged in orientation
  4. The F upside down

Explanation

Reflecting a 90° counter-clockwise rotation across a vertical axis reverses the rotation direction, producing a 90° clockwise rotation of the original. The reflection flips the handedness back to the clockwise orientation.