GCAT - General Cognitive Ability Test — Questions and Answers

Question 1: Hold these digits: 8, 1, 5, 3, 7. Now reverse them mentally. What is the middle digit of the reversed sequence?

1
7
5
3 (Correct answer)

Correct answer: 3

Reversed: 7, 3, 5, 1, 8 — the middle (3rd) digit is 5... wait: position 3 of 7,3,5,1,8 is 5.

Question 2: Which word does NOT belong with the others?

Brevity (Correct answer)
Courage
Perseverance
Tenacity

Correct answer: Brevity

Courage, tenacity, and perseverance all describe qualities of determined, resolute character. Brevity means shortness or conciseness — it is about length or duration, not strength of will.

Question 3: How many distinct ways can a standard 2×2 Rubik's cube face be oriented if you can only rotate the entire cube (not individual pieces)?

6
24 (Correct answer)
12
48

Correct answer: 24

A cube has 24 possible orientations (6 faces can be on top × 4 rotations per face).

Question 4: All carnivores eat meat. This creature does not eat meat. Which conclusion is valid?

This creature is an herbivore.
This creature might be a carnivore.
This creature is a carnivore.
This creature is not a carnivore. (Correct answer)

Correct answer: This creature is not a carnivore.

Contrapositive of 'all carnivores eat meat' is 'not eating meat means not a carnivore.'

Question 5: In a logic puzzle: P implies Q. Q implies R. R is false. What can you conclude about P?

P is false (Correct answer)
P is true
P implies R directly
P may be true or false

Correct answer: P is false

By contrapositive, not-R implies not-Q, and not-Q implies not-P, so P must be false.

Question 6: Find the missing number: 8 : 64 :: 5 : ___

50
15
25 (Correct answer)
10

Correct answer: 25

8 squared is 64; similarly, 5 squared is 25.

Question 7: A flat cross-shaped net is folded into a cube. If the center square is the bottom face, which square becomes the top face?

The square directly below the center (Correct answer)
The square to the left of the center
The square to the right of the center
The square directly above the center

Correct answer: The square directly below the center

When folding a cross-shaped net, the square opposite the bottom (directly below the center in the net) becomes the top face.

Question 8: Each row in a matrix contains three figures. The first figure has one dot inside, the second has two, and the third has three. The outer shape changes each row: row 1 = circle, row 2 = square, row 3 = triangle. What belongs in row 3, column 2?

Triangle with 2 dots (Correct answer)
Square with 2 dots
Circle with 2 dots
Triangle with 3 dots

Correct answer: Triangle with 2 dots

Row 3 uses triangles as the outer shape and column 2 always contains 2 dots.

Question 9: A 3×3 matrix uses three symbols: ●, ■, ▲. Each symbol appears exactly once per row and once per column. Row 1: ●, ■, ▲. Row 2: ■, ▲, ?. What is the missing symbol?

○
● (Correct answer)
■
▲

Correct answer: ●

Row 2 already has ■ and ▲, so the missing symbol must be ●.

Question 10: Find the next number: 729, 243, 81, 27, ?

6
9 (Correct answer)
12
3

Correct answer: 9

Each term is divided by 3, so 27 ÷ 3 = 9.

Question 11: Study these initials for 10 seconds: J.T., P.R., M.K., W.B., C.L., A.N. Which initials appeared FOURTH?

M.K.
P.R.
W.B. (Correct answer)
C.L.

Correct answer: W.B.

Counting: J.T.(1), P.R.(2), M.K.(3), W.B.(4) — the fourth set of initials is W.B.

Question 12: All A are B. Some B are C. No C are D. Which is a valid conclusion about A and D?

Some A are D.
All A are D.
No conclusion about A and D. (Correct answer)
No A are D.

Correct answer: No conclusion about A and D.

Since 'some B are C' is particular, we cannot determine whether any A fall in that subset, making a conclusion about A and D impossible.

Question 13: An ant walks along the outside of a cube from one corner to the diagonally opposite corner. The cube has side length 1. What is the shortest path the ant can walk?

2
√6
√5 (Correct answer)
3

Correct answer: √5

Unfolding two adjacent faces into a 2×1 rectangle, the straight-line distance across is √(1² + 2²) = √5.

Question 14: All valid arguments have true conclusions. This argument has a false conclusion. What follows?

This argument is valid.
This argument is not valid. (Correct answer)
All arguments with false conclusions are valid.
This argument might be valid.

Correct answer: This argument is not valid.

By contrapositive, a false conclusion means the argument is not valid.

Question 15: Identify the next term: 2, 6, 18, 54, 162, ?

486 (Correct answer)
648
384
324

Correct answer: 486

Each term is multiplied by 3, so 162 × 3 = 486.

Question 16: A 3D object is composed of stacked cubes. The front view shows a 2x2 square of cubes. The right-side view shows a column of two cubes on the left and a single cube on the right. Which of the following is the correct top-down view of the object?

A 2x2 square with the bottom-left quadrant empty.
A 2x2 square with the top-left quadrant empty.
A 2x2 square with all quadrants filled.
A 2x2 square with the bottom-right quadrant empty. (Correct answer)

Correct answer: A 2x2 square with the bottom-right quadrant empty.

The front view establishes a 2x2 footprint with at least one cube in each column. The right-side view shows that the back column is two cubes high and the front column is one cube high. This means from the top, you would see the two cubes in the back row and only one in the front row. The single cube in the front row corresponds to the single cube seen from the right-side view, meaning the bottom-right position (front-right from a top view) is empty. Therefore, the object consists of three cubes in an 'L' shape when viewed from the top.

Question 17: Find the next letter in the following series: B, C, E, H, L, ?

R
Q (Correct answer)
P
O

Correct answer: Q

The pattern is based on the increasing number of positions moved forward in the alphabet. From B to C is a step of 1. From C to E is a step of 2. From E to H is a step of 3. From H to L is a step of 4. Therefore, the next step must be 5. Five letters after L is Q.

Question 18: Which research design best controls for bias when testing whether a new drug is effective?

Give the drug to all willing participants and ask if they feel better
Give the drug to the sickest patients and compare their recovery to healthy people
Randomly assign participants to drug or placebo groups with neither group knowing which they received (Correct answer)
Give the drug to patients who request it and compare them to those who do not

Correct answer: Randomly assign participants to drug or placebo groups with neither group knowing which they received

A double-blind randomized controlled trial eliminates selection bias and placebo effects, providing the most reliable causal evidence.

Question 19: Which pair comes next? AA, CC, EE, GG, ___

JJ
II (Correct answer)
HH
KK

Correct answer: II

Each pair skips one letter (+2 positions), so after GG comes II.

Question 20: Which word does NOT belong with the others?

Theorem (Correct answer)
Metaphor
Alliteration
Simile

Correct answer: Theorem

Simile, metaphor, and alliteration are all figures of speech or literary devices used in writing and rhetoric. A theorem is a proven proposition in mathematics or logic — it belongs to a different field entirely.

Question 21: Verbal Reasoning - sentence completion. Choose the word that, when inserted in the sentence to replace the blank, best fits the meaning of the sentence. Electronic information and automated systems are essential to ____ all major federal operations.

Virtually (Correct answer)
Approximately
Fundamentally
Effectively
Implicitly

Correct answer: Virtually

The sentence refers to electronic information that is fundamental to (something) all major federal operations. The sentence's general idea implies that electronic information is essential to practically / nearly / almost all primary federal operations. Therefore, the only word accurately reflecting that meaning in the sentence's context is "virtually".

Question 22: What comes next: 256, 64, 16, 4, ?

3
1 (Correct answer)
2
0

Correct answer: 1

Each term is divided by 4, so 4 ÷ 4 = 1.

Question 23: Read the following paragraph: 'All servers updated with the new security patch must be rebooted. Some of the servers in the main datacenter were not updated with the new security patch. Server-05 is in the main datacenter and was not rebooted.' Based strictly on this information, which conclusion can be logically drawn?

All servers that were not rebooted are in the main datacenter.
No server in the main datacenter was rebooted.
Server-05 was updated with the new security patch.
Server-05 was not updated with the new security patch. (Correct answer)

Correct answer: Server-05 was not updated with the new security patch.

The rule is: if a server was updated, it must be rebooted. We know Server-05 was *not* rebooted. Using logical deduction (the contrapositive), if the consequence (reboot) did not happen, then the initial condition (being updated) must also not have happened. Therefore, Server-05 was not updated. We cannot make broad conclusions about all servers in the datacenter, only about Server-05 specifically.

Question 24: What number is next? 3, 9, 27, 81, ___

324
256
162
243 (Correct answer)

Correct answer: 243

Each term is multiplied by 3 (powers of 3), so 81 × 3 = 243.

Question 25: All squares are rectangles. All rectangles are parallelograms. Some parallelograms are rhombuses. Which is definitely true?

Some squares are rhombuses.
Some rectangles are squares.
All squares are parallelograms. (Correct answer)
All squares are rhombuses.

Correct answer: All squares are parallelograms.

Squares ⊆ rectangles ⊆ parallelograms, so all squares are parallelograms.

Question 26: No mammals lay eggs. Platypuses lay eggs. What must follow?

Platypuses are mammals.
Some mammals lay eggs.
Platypuses are not mammals. (Correct answer)
Platypuses might be mammals.

Correct answer: Platypuses are not mammals.

By contrapositive, if something lays eggs it cannot be a mammal.

Question 27: All red objects are heavy. This ball is not heavy. What follows?

This ball is red.
This ball might be red.
This ball is sometimes red.
This ball is not red. (Correct answer)

Correct answer: This ball is not red.

By contrapositive: if not heavy, then not red.

Question 28: A report shows that a warehouse processed 1,250 orders last month with a 96% accuracy rate. How many orders contained errors?

75
60
50 (Correct answer)
40

Correct answer: 50

Error rate = 4%; 4% of 1,250 = 0.04 × 1,250 = 50 orders with errors.

Question 29: Some roses are red. All red flowers are beautiful. Which must be true?

No roses are beautiful.
Some roses are beautiful. (Correct answer)
All roses are beautiful.
All beautiful things are roses.

Correct answer: Some roses are beautiful.

The red roses must be beautiful, making at least some roses beautiful.

Question 30: A student argues: 'My teacher gives hard tests and I failed; therefore the test was unfair.' What flaw does this argument contain?

It assumes that difficulty is equivalent to unfairness (Correct answer)
It correctly identifies the teacher as the cause of failure
It relies on a false dichotomy between hard and easy
It uses circular reasoning by restating the premise

Correct answer: It assumes that difficulty is equivalent to unfairness

Confusing difficulty with unfairness is an unwarranted assumption — a test can be challenging and still fairly measure the required knowledge.

Question 31: Exactly three of the five statements below are true. Statement 3 says 'Statement 1 is false.' If Statement 1 is true, how many of statements 2–5 must be true?

3
1
2 (Correct answer)
4

Correct answer: 2

If Statement 1 is true, then Statement 3 is false; with 3 total true among 5 and statements 1 and 3 accounting for one true and one false, exactly 2 more from statements 2, 4, 5 must be true.

Question 32: An inspector checks parts and records defects. She checks 12 parts, finds defects on parts 2, 5, 8, and 11. What pattern do the defective part numbers follow?

Every 2nd part
Every 3rd part starting from 2 (Correct answer)
Every 4th part
Random defects

Correct answer: Every 3rd part starting from 2

The defective parts are 2, 5, 8, 11 — each is 3 more than the previous, starting at 2.

Question 33: A car travels 240 miles on 8 gallons of gas. At the same rate, how many miles can it travel on 11 gallons?

320
330 (Correct answer)
308
286

Correct answer: 330

Fuel efficiency = 240 ÷ 8 = 30 mpg; 30 × 11 = 330 miles.

Question 34: Some managers are leaders. All leaders are communicators. Which must be true?

All communicators are managers.
No managers are communicators.
Some managers are communicators. (Correct answer)
All managers are communicators.

Correct answer: Some managers are communicators.

The managers who are leaders must also be communicators, so at least some managers are communicators.

Question 35: A sequence of overlapping shapes shows: circle overlapping square (circle in front), square overlapping triangle (square in front), triangle overlapping circle (triangle in front). What is the layering rule?

The darker shape is always in front
Each shape takes a turn being in front in rotation (Correct answer)
Each shape alternates between front and back
The larger shape is always in front

Correct answer: Each shape takes a turn being in front in rotation

Circle, square, and triangle each take exactly one turn being the front shape in a rotating sequence.

Question 36: You are given three separate 2D shapes: two identical right-angled triangles and one small square. The length of the two shorter sides of the triangles is equal to the side length of the square. Which of the following composite shapes can be formed by fitting these three pieces together without any overlap?

A larger right-angled triangle.
A regular pentagon.
A larger square.
A parallelogram. (Correct answer)

Correct answer: A parallelogram.

The two right-angled triangles can be joined along their hypotenuses to form a rectangle that is twice as long as it is wide. However, to use all three pieces, you can place the two triangles together along one of their shorter sides to form a larger triangle. Then, place the square adjacent to the combined side. A more direct assembly is to place the hypotenuse of each triangle against opposite sides of the square, forming a parallelogram.

Question 37: ANCHOR : SHIP :: STAKE : ?

Flag
Tent (Correct answer)
Rope
Boat

Correct answer: Tent

An anchor is used to secure a ship in place, just as a stake is used to secure a tent in place.

Question 38: A factory finds that 3 out of every 100 widgets are defective. If the factory produces 2,500 widgets, how many are expected to be defective?

100
75 (Correct answer)
250
25

Correct answer: 75

3% of 2,500 = 0.03 × 2,500 = 75 defective widgets expected.

Question 39: In the gear system shown, the driver gear 'A' rotates clockwise. Gear 'A' meshes with gear 'B'. Gear 'B' and gear 'C' are fixed on the same axle. Gear 'C' meshes with gear 'D'. In which direction will gear 'D' rotate?

Clockwise. (Correct answer)
The direction depends on the gear sizes.
Counter-clockwise.
It will not rotate.

Correct answer: Clockwise.

When two gears mesh, they rotate in opposite directions. Since gear 'A' rotates clockwise (CW), gear 'B' will rotate counter-clockwise (CCW). Because gears 'B' and 'C' are on the same axle, gear 'C' also rotates counter-clockwise (CCW). Since gear 'C' (CCW) meshes with gear 'D', gear 'D' will rotate in the opposite direction, which is clockwise (CW).

Question 40: NOVEL : CHAPTER :: SYMPHONY : ?

Theme
Note
Movement (Correct answer)
Measure

Correct answer: Movement

A novel is divided into chapters, and a symphony is divided into movements.

Question 41: You are told: 'If it rains, cancel the meeting; if the meeting is cancelled, notify the team.' It rains. What must happen?

Do nothing
Notify the team only
Cancel the meeting only
Cancel the meeting and notify the team (Correct answer)

Correct answer: Cancel the meeting and notify the team

Rain triggers cancellation, which in turn triggers team notification — both actions follow.

Question 42: MANUSCRIPT : PUBLISH :: ORE : ?

Sell
Refine (Correct answer)
Mine
Transport

Correct answer: Refine

A manuscript must be published to become a final product, just as ore must be refined to yield usable metal.

Question 43: In a pattern matrix, each cell contains filled squares. Row 1 has 1, 2, 3 filled squares. Row 2 has 2, 4, 6 filled squares. Row 3 has 3, 6, ? filled squares.

12
7
9 (Correct answer)
8

Correct answer: 9

Each cell equals (row number) × (column number): 3 × 3 = 9.

Question 44: A team must finish a project in 10 days. They complete 40% in the first 4 days. At this rate, will they finish on time?

Yes, they are exactly on track (Correct answer)
Cannot be determined without more data
No, they are behind schedule
Yes, they are ahead of schedule

Correct answer: Yes, they are exactly on track

40% in 4 days equals 10% per day, so the remaining 60% takes 6 more days, completing on day 10 exactly on schedule.

Question 45: A pattern of tiles uses only squares and regular octagons with equal side lengths, fitting together without gaps. How many sides does each octagon share with squares?

2
6
8
4 (Correct answer)

Correct answer: 4

In the standard square-octagon tiling, each octagon shares 4 of its 8 sides with squares (alternating sides).

Question 46: Which number does NOT fit the quickly-scanned pattern: 14, 21, 28, 35, 43, 49?

49
35
21
43 (Correct answer)

Correct answer: 43

The pattern increases by 7 each time; 35 + 7 = 42, not 43.

Question 47: A square is rotated 45° and placed inside a larger square so that its corners touch the midpoints of the larger square's sides. What fraction of the larger square does the rotated square cover?

1/2 (Correct answer)
2/3
3/4
1/3

Correct answer: 1/2

A square rotated 45° with corners at the midpoints of a larger square covers exactly half the larger square's area.

Question 48: A project takes 12 days with 8 people. If 4 people leave after 6 days, how many more days are needed?

6
12
8
10 (Correct answer)

Correct answer: 10

Total work = 96 person-days; 6 days × 8 people = 48 done; remaining 48 ÷ 4 people = 12 more days.

Question 49: Read the following statements: 1. All engineers are proficient with computers. 2. Some people who are proficient with computers are also artists. Based only on these statements, which of the following conclusions is logically valid?

All artists are proficient with computers.
All people proficient with computers are engineers.
Some engineers are artists.
A conclusion cannot be logically drawn. (Correct answer)

Correct answer: A conclusion cannot be logically drawn.

The premises establish that engineers are a subset of 'people proficient with computers'. They also state that the group 'artists' has some overlap with 'people proficient with computers'. However, we do not know if the artist overlap includes any engineers. The artists who are proficient with computers could be entirely separate from the engineers. Therefore, no certain conclusion can be drawn about the relationship between engineers and artists.

Question 50: How many times does the digit '3' appear in the following list: 13, 33, 73, 103, 130, 333?

9 (Correct answer)
6
8
10

Correct answer: 9

Counting each digit: 13(1), 33(2), 73(1), 103(1), 130(1), 333(3) = 9 threes total.

Question 51: Complete the series: 64, 32, 16, 8, 4, ?

4
1
3
2 (Correct answer)

Correct answer: 2

Each term is halved (divided by 2), so 4 ÷ 2 = 2.

GCAT - General Cognitive Ability Test

The GCAT, developed by Podium Systems, is a BPS/EFPA-registered psychometric assessment measuring general mental ability across verbal reasoning, numerical reasoning, and abstract reasoning domains. It is widely used in recruitment and talent development.

Questions

30 min

Time Limit

50%

To Pass

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