1
Classify the provided figures into three distinct groups, ensuring each figure is used only one time.
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Solution: Step 1: Identify figures that are geometrical, contain line segments (half the number of sides of the figure) parallel to the sides of the figure. Figures 3, 6, and 9 fit this description.
Step 2: Identify figures consisting of a circle intersecting a triangle, where the triangle is divided into two equal parts by a straight line. Figures 1, 5, and 8 belong to this group.
Step 3: Identify figures that are funnel-shaped. Figures 2, 4, and 7 constitute the third category.
2
Classify the given figures into three groups, utilizing each figure just once.
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Solution: Step 1: Identify figures that contain a V-shaped element inside a geometric figure. Figures 1 and 3 meet this criterion.
Step 2: Identify figures that have two similar elements, where one is placed inside the other and touches it. Figures 2, 4, and 5 form this group.
Step 3: Identify figures that are geometric and divided into four equal parts by two mutually perpendicular straight lines. Figures 6 and 7 belong to the third category.
10
Group the provided figures into three distinct classes, using each figure only once.
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Solution: Step 1: Identify figures that are undivided geometrical shapes. Figures 1, 7, and 8 belong to this category.
Step 2: Identify figures that are geometrical and divided into two parts. Figures 3, 5, and 6 fit this description.
Step 3: Identify figures that are geometrical and divided into four parts. Figures 2, 4, and 9 form the third class.
12
Categorize the provided figures into three distinct classes, using each figure only one time.
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Solution: Step 1: Identify figures with patterns formed by four lines curved in a concave direction. Figures 1, 2, and 5 fit this description.
Step 2: Identify figures with patterns formed by four lines curved in a convex direction. Figures 3, 7, and 8 belong to this group.
Step 3: Identify figures with patterns formed solely by straight lines. Figures 4, 6, and 9 constitute the third class.
15
Select the figure that is distinct from the other given figures.
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Solution: Step 1: Analyze the arrangement of parallel lines (one, two, and three) within each figure.
Step 2: Determine the sequence and direction of these parallel lines in figures 1, 2, 4, and 5. Observe that in these figures, the sequence of one, two, and three parallel lines consistently appears in an anticlockwise (ACW) direction.
Step 3: Examine figure (3). Notice that in this figure, the sequence of one, two, and three parallel lines appears sequentially in a clockwise (CW) direction.
Step 4: Conclude that figure (3) is different from the rest because its sequence of parallel lines follows a clockwise direction, unlike the others which follow an anticlockwise direction.
18
Classify the given figures into three distinct groups, ensuring each figure is used only once.
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Solution: Step 1: Identify figures that are two-dimensional quadrilaterals. Figures 1, 4, and 7 fall into this category.
Step 2: Identify figures that are three-dimensional. Figures 2, 5, and 8 belong to this group.
Step 3: Identify figures that are two-dimensional triangles. Figures 3, 6, and 9 form the third group.
19
Categorize the provided figures into three groups, utilizing each figure only once.
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Solution: Step 1: Identify figures that are simple geometric shapes. Figures 1, 2, and 7 belong to this group.
Step 2: Identify figures that have one element placed inside a different element. Figures 3, 5, and 9 fit this description.
Step 3: Identify figures that have two different elements attached to each other. Figures 4, 6, and 8 form the third category.
20
Categorize the given figures into three distinct groups, utilizing each figure precisely once.
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Solution: Step 1: Observe all the given figures (1-9) carefully to identify common characteristics or internal structures.
Step 2: Identify figures where one element is placed inside another different element. These are figures 1, 3, and 9.
Step 3: Identify figures containing two mutually perpendicular lines that divide the figure into four parts. These are figures 2, 5, and 6.
Step 4: Identify figures with two similar elements (unequal in size) attached to each other. These are figures 4, 7, and 8.
Step 5: Form three classes: (1, 3, 9), (2, 5, 6), and (4, 7, 8).
Step 6: Compare this grouping with the given options to find the correct one.