Non Verbal Reasoning · Figures & Shapes
Shape Construction — Questions & Answers
Shape construction questions give five pieces and ask which three fit together to form a complete square. Pieces may be turned; look for straight outer edges and right-angled corners.
- 5 solved questions
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How to approach
Pieces with straight edges and right-angled corners give the square's sides and corners.
Cut edges must match exactly — the same length and angle on both pieces.
Watch for decoys: a smaller copy of a piece, or a piece with one corner moved.
5 solved Shape Construction questions
Which three of the five pieces below fit together (turned as needed) to form a complete square?
Solution — answer B
Pieces 1, 4, 5 fit together into the square: their straight outer edges make its four sides and their cut edges match up exactly. Piece 2 looks like piece 5 but is smaller, and piece 3 is piece 4 with one corner moved, so any choice using them leaves a gap or an overlap.
5 steps · reveal one at a timeStep 1: Understand the Goal
The task is to identify which three of the five available pieces can be rotated and assembled to form a perfect square. We need to find the specific combination that works.
Step 2: Find the Fitting Pieces
The verified solution states that pieces 1, 4, and 5 are the correct combination. When these three pieces are turned as needed, their straight outer edges will form the four sides of the complete square.
Step 3: Confirm the Fit
For pieces 1, 4, and 5, not only do their outer edges form the square, but their cut edges also match up exactly. This ensures there are no gaps or overlaps when they are put together.
Step 4: Rule Out Others
The solution also clarifies why other pieces don't work. Piece 2 is described as a smaller version of piece 5, and piece 3 is like piece 4 but with a corner moved. Using these would create gaps or overlaps.
Step 5: The answer
So the answer is (B) 1, 4, 5. This combination is confirmed to form a complete square with no gaps or overlaps, unlike any other grouping involving pieces 2 or 3.
Which three of the five pieces below fit together (turned as needed) to form a complete square?
Solution — answer A
Pieces 1, 4, 5 fit together into the square: their straight outer edges make its four sides and their cut edges match up exactly. Piece 3 looks like piece 5 but is smaller, and piece 2 is piece 4 with one corner moved, so any choice using them leaves a gap or an overlap.
4 steps · reveal one at a timeStep 1: Understand the Goal
The task is to identify which three of the five given pieces can be turned and fit together perfectly to form a complete square. We need to find the specific combination that works.
Step 2: Identify Fitting Pieces
According to the solution, pieces 1, 4, and 5 are the ones that fit together. Their straight outer edges form the four sides of the square, and their cut edges match up exactly to complete the shape.
Step 3: Rule Out Other Pieces
Piece 3 is described as looking like piece 5 but is smaller, meaning it wouldn't fit correctly. Piece 2 is described as piece 4 with one corner moved, which would also cause a gap or an overlap.
Step 4: The Answer
So the answer is (A) 1, 4, 5. These three pieces are confirmed to fit together perfectly, forming a complete square without gaps or overlaps, unlike combinations involving pieces 2 or 3.
Which three of the five pieces below fit together (turned as needed) to form a complete square?
Solution — answer D
Pieces 1, 3, 5 fit together into the square: their straight outer edges make its four sides and their cut edges match up exactly. Piece 4 looks like piece 3 but is smaller, and piece 2 is piece 5 with one corner moved, so any choice using them leaves a gap or an overlap.
5 steps · reveal one at a timeStep 1: Understand the Task
The goal is to identify which three of the five given pieces can be arranged to form a complete square. We need to find the correct set of pieces that fit together perfectly.
Step 2: Examine the Correct Pieces
The verified solution states that pieces 1, 3, and 5 are the ones that fit together. Their straight outer edges form the four sides of the square, and their cut edges align precisely to complete the shape.
Step 3: Consider Other Pieces
The solution explains why other pieces don't work. Piece 4 is described as similar to piece 3 but smaller. Piece 2 is like piece 5, but with one corner moved. These differences prevent them from fitting correctly.
Step 4: Identify Mismatches
Because pieces 2 and 4 have different shapes or sizes compared to pieces 3 and 5, any combination including them would result in either gaps or overlaps when trying to form a complete square. Only pieces 1, 3, and 5 fit perfectly.
Step 5: The answer
So the answer is (D) 1, 3, 5. This combination is the only one where the pieces' straight outer edges form the square's sides and their cut edges match exactly, as confirmed by the solution.
Which three of the five pieces below fit together (turned as needed) to form a complete square?
Solution — answer C
Pieces 1, 3, 5 fit together into the square: their straight outer edges make its four sides and their cut edges match up exactly. Piece 2 looks like piece 5 but is smaller, and piece 4 is piece 1 with one corner moved, so any choice using them leaves a gap or an overlap.
4 steps · reveal one at a timeStep 1: Understand the Goal
The question asks you to find which three of five given pieces can be arranged and combined to form a complete square. This is a spatial reasoning puzzle.
Step 2: Identify Correct Pieces
According to the solution, pieces 1, 3, and 5 are the ones that successfully fit together. Their straight outer edges form the four sides of the square, and their cut edges align perfectly.
Step 3: Rule Out Other Pieces
The solution explains why other pieces don't work. Piece 2 is similar to piece 5 but is smaller, which would leave a gap. Piece 4 is like piece 1, but with a corner moved, causing a gap or overlap.
Step 4: The answer
So the answer is (C) 1, 3, 5. These specific pieces are confirmed to fit together precisely to form the complete square, while using other pieces would result in an incomplete or incorrect shape.
Which three of the five pieces below fit together (turned as needed) to form a complete square?
Solution — answer A
Pieces 1, 2, 5 fit together into the square: their straight outer edges make its four sides and their cut edges match up exactly. Piece 4 looks like piece 2 but is smaller, and piece 3 is piece 5 with one corner moved, so any choice using them leaves a gap or an overlap.
5 steps · reveal one at a timeStep 1: Understand the Task
The goal is to find which three of the five given pieces can be turned and fitted together perfectly to form a complete square. We need to identify the correct combination of pieces.
Step 2: Identify Fitting Pieces
The verified solution states that pieces 1, 2, and 5 are the ones that fit together to form the square. This is the key insight for solving the problem.
Step 3: Confirm the Fit
When pieces 1, 2, and 5 are assembled, their straight outer edges correctly form the four sides of the square. Crucially, their cut edges match up exactly without any gaps or overlaps, creating a complete shape.
Step 4: Rule Out Other Pieces
Piece 4 is described as being similar to piece 2 but is smaller, meaning it would leave a gap. Piece 3 is like piece 5 but has a corner moved, which would cause an overlap or an incorrect fit. Therefore, any combination using pieces 3 or 4 will not work.
Step 5: The answer
So the answer is (A) 1, 2, 5. This combination is the only one where the pieces fit together perfectly to form a complete square, as confirmed by their matching edges and the issues with other pieces.
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