Practice tests · GATE

GATE analytical and spatial aptitude: 5 practice questions

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Analytical aptitude in GATE means logical reasoning: deduction from statements, analogies, number patterns and arrangement puzzles. Spatial aptitude, the fourth GA skill, tests paper folding, cutting, patterns and 3D shapes. Both reward a calm, systematic method over speed. The five original questions below mix the two.

What analytical and spatial aptitude cover

The GATE 2027 syllabus describes analytical aptitude as deduction and induction, analogy and numerical reasoning, and spatial aptitude as transformations, paper folding and cutting, and 2D and 3D patterns. In question form that gives you:

• Statement-conclusion questions (what must be true, what cannot be).
• Number and letter series with a non-obvious rule.
• Seating, ordering and scheduling puzzles with a unique answer.
• Clock, calendar and direction problems.
• Cube cutting and painting, paper folding and punching, and counting shapes.

All five questions here are MCQs, and a wrong MCQ answer in the real paper costs 1/3 or 2/3 of the question's marks. The GATE general aptitude guide shows where GA sits in the 100-mark paper.

Practice questions

Question 1

All engineers are logical. Some logical people are artists. No artist is careless. Which one of the following must be true?

• A. Some artists are logical.
• B. Some engineers are artists.
• C. No engineer is careless.
• D. All logical people are engineers.

Question 2

What is the next term in the series 3, 8, 18, 38, 78, ?

• A. 148
• B. 156
• C. 158
• D. 160

Question 3

Five friends P, Q, R, S and T sit in a row facing north. P sits at the left end and S sits at the right end. T sits immediately to the left of Q. R does not sit next to Q. Who sits in the middle?

• A. Q
• B. R
• C. S
• D. T

Question 4

What is the angle between the hour hand and the minute hand of a clock at 3:20?

• A. 30 degrees
• B. 20 degrees
• C. 10 degrees
• D. 0 degrees

Question 5

A solid cube is painted on all six faces and then cut into 27 identical smaller cubes (3 × 3 × 3). How many of the smaller cubes have exactly two painted faces?

• A. 6
• B. 8
• C. 12
• D. 24

Answers and explanations

1. A. "Some logical people are artists" is the same statement as "Some artists are logical", so A must be true. B does not follow, because the engineers may be a different group of logical people from the artists. C does not follow because nothing links engineers to carelessness. D reverses the first statement ("All engineers are logical" does not give "all logical are engineers").
2. C. The differences are 5, 10, 20, 40, so the next difference is 80 and the next term is 78 + 80 = 158. The same rule can be written as each term = 2 × previous term + 2 (3, 8, 18, 38, 78, 158).
3. D. Positions 1 to 5 from the left: P is in 1 and S in 5. Q, R and T fill positions 2 to 4. "T immediately left of Q" allows T2-Q3 or T3-Q4. If T2-Q3, R takes 4 and sits next to Q, which is not allowed. So T3-Q4 and R2, giving P R T Q S. T sits in the middle.
4. B. At 3:20 the minute hand is at 20 × 6 = 120 degrees from 12. The hour hand moves 0.5 degrees per minute, so it is at 3 × 30 + 20 × 0.5 = 100 degrees. The angle between them is 120 − 100 = 20 degrees. A common error is to put the hour hand exactly on the 3.
5. C. Only the 12 cubes at the middle of each edge of the big cube touch two outer faces, one per edge. The 8 corner cubes have three painted faces, the 6 face-centre cubes have one, and the single cube in the middle has none (8 + 12 + 6 + 1 = 27).

How to prepare analytical and spatial aptitude

• Write every statement as a diagram. For syllogisms, draw circles (Venn diagrams) and check each conclusion against all possible drawings. Only a conclusion that holds in every drawing "must be true", as in Question 1.
• For series, tabulate first differences, second differences and ratios, then test "2 × previous + constant" and squares or cubes plus an adjustment. Most series fall to one of these checks within thirty seconds.
• For arrangements, fix the certain positions first and then enumerate the rest. Write the cases explicitly and eliminate; do not try to keep the whole puzzle in your head.
• Learn the clock formula once: angle = |30H − 5.5M| degrees, where H is the hour and M the minutes. At 3:20 that is |90 − 110| = 20.
• For cubes, memorise the counting rule for an n × n × n cube: corners 8, edge cubes 12(n − 2), face cubes 6(n − 2)², inner cubes (n − 2)³.
• Practise paper folding by physically folding paper. Fold a sheet twice, punch one hole, and unfold it. A point not on a fold line gives 4 holes after two folds.

Give reasoning a fixed ten minutes a day alongside the other GATE general aptitude topics. The preparation strategy page explains where GA practice fits in a 6-month or 12-month plan.

Take the full topic test on PrepMatic

PrepMatic's topic tests run about 15 questions in 30 minutes, a good way to practise reasoning sets against the clock. If you are unsure whether GA or your branch subjects deserve the extra time, the free assessment shows your weakest subjects first.

← All practice tests