Short answer: For number series, look for changes, repeating operations and interleaved sequences. For paper folding, track each fold and unfold in reverse. These ten original questions cover five number patterns and five simplified folding problems. They are teaching exercises, not official GAN questions.
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Original GAN-style practice, not official GAN questions.
Two methods, kept separate
GAN’s public website describes basic math, reading and spatial skills. Nashville, Phoenix and Kalamazoo list five areas, including Numerical Reasoning and Paper Folding. Some programs, including Minneapolis, publish a sixth Problem Solving area. Do not assume another program’s section list applies to yours. These original questions do not establish official item types, lengths or scoring rules.
| Type | First move | Check | Frequent error |
|---|---|---|---|
| Differences | Subtract consecutive terms | Explain every gap | Forcing one constant step |
| Alternating | Write operations above gaps | Repeat the full cycle | Stopping at one match |
| Interleaved | Read odd and even positions separately | Continue both subseries | Treating all terms as one line |
| Paper folding | Number folds | Undo last fold first | Opening in original order |
| Punch on crease | Mark its relation to each line | On-line point stays one point | Duplicating across the crease |
Number series questions
Question 1
18, 23, 21, 26, 24, ?
A. 27 B. 28 C. 29 D. 31
Answer: C, 29. Steps repeat plus 5, minus 2. From 24, add 5. Every displayed gap fits the cycle.
Question 2
4, 7, 13, 22, 34, ?
A. 43 B. 46 C. 49 D. 52
Answer: C, 49. Differences are 3, 6, 9 and 12. They grow by 3, so the next difference is 15. Add 15 to 34.
Question 3
2, 30, 4, 27, 8, 24, 16, ?
A. 18 B. 20 C. 21 D. 32
Answer: C, 21. Odd positions are 2, 4, 8, 16 and double. Even positions are 30, 27, 24 and fall by 3. The next even value is 21.
Question 4
6, 11, 18, 27, 38, ?
A. 49 B. 50 C. 51 D. 52
Answer: C, 51. Differences are 5, 7, 9 and 11. The next difference is 13, so 38 plus 13 equals 51.
Question 5
81, 27, 9, 3, ?
A. 0 B. 1 C. 2 D. 6
Answer: B, 1. Divide by 3 each time. The chain is 81, 27, 9, 3, 1. Subtraction does not explain every step.
Paper folding text questions
These five exercises use an ideal point model to teach symmetry. A punch is represented by a point with no width, and the answer counts distinct point locations after unfolding. A point exactly on a fold line stays in the same location when reflected across that line. Real punches have width and may create notches at folded edges; these text exercises do not model hole size or edge shape.
Translate each sentence into a fold record. Write F1 for the first crease and F2 for the second. When unfolding, handle F2 before F1.
Question 6
A square is folded once along a vertical center line. One hole is punched away from the line. How many positions appear after opening?
A. 1 B. 2 C. 3 D. 4
Answer: B, 2. The punch is away from the crease, so opening mirrors it. One original and one mirror give two.
Question 7
A square is folded vertically and then horizontally. A hole is punched away from both lines. How many positions appear after opening?
A. 2 B. 3 C. 4 D. 8
Answer: C, 4. Undo the horizontal fold first, doubling one position to two. Undo the vertical fold next, doubling two to four.
Question 8
In an ideal point-symmetry model, a square is folded along its vertical center line and then its horizontal center line. A marked point lies exactly on the horizontal fold line but away from the vertical fold line. How many distinct point locations appear after both folds are opened?
A. 1 B. 2 C. 3 D. 4
Answer: B, 2. Reflection across the horizontal line leaves the point unchanged. Reflection across the vertical line creates one additional location, giving two distinct points.
Question 9
A rectangle is folded left to right. Two separate holes are punched away from the crease and their mirrors do not overlap. How many positions appear?
A. 2 B. 3 C. 4 D. 8
Answer: C, 4. Each punch creates one distinct mirror. Two original positions plus two mirrors produce four.
Question 10
In an ideal point-symmetry model, a square is folded along its vertical center line and then its horizontal center line. A marked point lies exactly at the intersection of both fold lines. How many distinct point locations appear after both folds are opened?
A. 1 B. 2 C. 3 D. 4
Answer: A, 1. The point is unchanged by reflection across either line because it lies on both lines. One distinct location remains. This is a geometry exercise, not a physical hole punched through a folded corner.
First steps for a series
Copy the terms with room between them. Write first differences. If they do not form a useful rule, test alternating operations, ratios, or odd and even positions. Do not accept a pattern unless it explains every transition. A rule that fits only the final two terms is not enough.
When differences grow, inspect their own differences. Question 2 has 3, 6, 9, 12, so that second level changes by a constant 3. Question 4 has consecutive odd differences. Writing the gaps prevents an attractive but incomplete pattern from winning.
For alternating patterns, write each operation over its gap. For interleaved patterns, copy odd positions onto one line and even positions onto another. Question 3 looks irregular until those two lines are separated.
First steps for a fold
Number folds in the order shown. Mark whether the punch is on or away from every crease. Undo the last fold first. Mirror only across a crease that does not contain the punch. After each opening, count distinct positions and check overlap.
A point exactly on a crease remains on that crease when opened. It does not create two locations. With two folds, that fact must be checked separately for both lines. A point can be on one crease but away from the other, as in question 8.
Common wrong approaches
Stopping at a plausible pattern. Several rules can fit two gaps. Use every term. Question 3 becomes clear only after odd and even positions are separated.
Mixing operations without a cycle. If you propose alternating steps, write the full repeating cycle and verify it at least twice where the terms allow.
Doubling for every fold. A point on a crease does not duplicate across that crease. Question 10 stays at one position despite two folds.
Opening in the same order. Physical unfolding reverses the folding sequence. The last fold made opens first.
Ignoring overlap. Mirrored positions can coincide in some drawings. Count distinct final positions, not mirror operations.
Build new practice without copying
Change one feature and solve again. For question 1, use plus 6 and minus 3. For question 4, begin at 5 but keep the odd differences. For question 7, put the punch on one crease and predict two positions instead of four. For question 9, use an ideal point model. Put one marked point exactly on the crease and the other away from it. If the off-crease point and its reflection are distinct from the crease point, the unfolded pattern contains three distinct locations.
Explain each rule before checking the number. Then reverse the process: create a short sequence from a written rule, or describe a two fold setup that produces four distinct positions. This tests the relationship rather than memory.
Reading a complete paper-folding diagram
Confirm the first fold, second fold, folded-paper orientation and marked location before unfolding in reverse. Track coordinates, not only the final count, because answer choices can contain the same number of points in different positions. If fold direction or the marked location is missing, the result may not be unique.
Original coordinate practice
A square uses coordinates from -2 to 2 on each axis. Fold the left half to the right across x = 0, then fold the bottom half upward across y = 0. On the folded quarter, mark the point (1, 1). Which set appears after both folds open?
A. {(1, 1), (-1, 1), (1, -1), (-1, -1)}
B. {(1, 1), (-1, 1)}
C. {(1, 1), (1, -1)}
D. {(1, 1), (-1, -1)}
Answer: A. Undo the horizontal fold to add (1, -1). Then undo the vertical fold to reflect both points to (-1, 1) and (-1, -1). Four positions appear. This coordinate model replaces a drawing; an actual diagram question must show equivalent fold directions and point placement.
Timing without guessing a national limit
The official pages checked here do not establish one national time for these sections. Use small sets to record your own pace, then use the schedule in your program notice for a full simulation. Accuracy comes first while learning the method. Add timing only after you can explain the rule or fold sequence.
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Sources checked October 2026
- GAN: https://ganhumanresources.com/gan-aptitude-test
- Nashville: https://www.nejatc.org/test-prep
- Kalamazoo: https://www.kalamazoojatc.com/apply/
- Phoenix: https://pejatc.org/how-to-apply/
- iPREP: https://www.iprep.online/courses/gan-aptitude-practice-test/
