 # Grouping of Figures

In Grouping of Figures, different figures are put together on the basis of a certain rule, pattern or property. Here in this section on the grouping of figures, we will solve many questions that are similar to the previous year questions and concepts. In these questions, a given set of figures will be featured. Some of these figures can be grouped together while as others can’t be. The task is to find out the rules and/or similarities between each individual set. Let us see some of the solved examples and the concepts below.

## Grouping of Figures

In this type of questions, you are given a set of usually 6, 7 or 9 etc. figures, which are numbered. The candidate is required to analyse these figures and classify them into groups consisting of figures having more or less the same properties.

The candidate is required to analyse these figures and classify them into groups consisting of figures having more or less than the same properties. The best answer is to be selected from a given set of fairly close alternatives.

## Solved Examples For You

### Part A

Directions: In each of the following question, group the given figures into three classes using each figure only once.

Example 1: Problem Figure: 1. (7, 8, 9) (2, 4, 3) (1, 5, 6)
2. (1, 3, 3) (4, 5, 7) (6, 8, 9)
3. (1, 6, 8) (3, 4, 7) (2, 5, 9)
4. (1, 6, 9) (3, 4, 7) (2, 5, 8)
5. none of the above

Answer: The figures (1), (6) and (9) are all triangles while as the figures (3), (4) and (7) are all quadrilaterals. Also, the figures (2), (5) and (8) are all pentagons. So these groups are identical and the correct answer is thus D.

Directions: There are two classes of three figures each. Class ‘A’ figures differ in a certain way from the figures in class ‘B’. Which of the four answer figures belong to class ‘A’?

Example 2: Problem Figure:  1. Both (1) and (3)
2. (1) and (2) both
3. Both (2) and (4)
4. (2) and (3) only
5. none of the above

Answer: The answer here is very simple. Each figure in class A consists of two similar closed figures, which are placed one inside the other. Therefore the answer is that (2) and (3) both are correct and the correct option is D. (2) and (3) only.

Let us see more solved examples on the Grouping of Figures.

### Part B

Example 3: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: 1. (1, 3, 4) (2, 5, 9) (6, 7, 8)
2. (1, 2, 3) (4, 5, 6) (7, 8, 9)
3. (1, 5, 9) (2, 4, 7) (3, 6, 8)
4. (3, 7, 8) (1, 6, 5) (4, 2, 9)
5. none of the above

Answer: If we start grouping the figures on the basis of sides, we have:

The figures that are made by three lines are (1, 3, 4)

Also, the figures which are made by four lines are (6, 7, 8)

Similarly, the figures made by the five lines are (2, 5, 9). These three groups are present in the option A. Thus the answer is A.

Example 4: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: 1. (1, 4, 7) (2, 5, 8) (3, 6, 9)
2. (1, 3, 6) (2, 5, 8) (4, 7, 9)
3. (1, 2, 4) (3, 5, 8) (6, 7, 9)
4. (1, 4, 9) (2, 5, 8) (3, 6, 7)
5. none of the above

Answer: There are figures that have one small and one big circle are figure 1, figure 4, and figure 7. Figures which have one sharp point are the figure2, figure 5, and figure 8. Also, the figures that have shapes like buckets are the figure 3, figure 6, and figure 9.

### Part C

Example 5: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: [SSC (CGL) 2002]

1. (1, 2, 3) (4, 8, 9) (5, 7, 6)
2. (4, 5, 7) (3, 1, 2) (7, 8, 9)
3. (1, 2, 7) (8, 9, 4) (2, 3, 6)
4. (3, 5, 6) (8, 7, 4) (9, 1, 2)
5. none of the above

Answer: The figures 1, 3 and 7 have three petals.three rectangles and three triangles respectively. So, they should be grouped in one group figures 4, 8 and 9 have one triangle, one rectangle and one circle respectively. So, they should be grouped into one group. On the other hand, the figures between 2, 5 and 6 have five petals, five triangles and five squares, respectively. So, they should be grouped into one group. Therefore the correct answer is C. (1, 2, 7) (8, 9, 4) (2, 3, 6).

Example 6: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: 1. (1, 4, 8) (2, 5, 7) (3, 9, 6)
2. (1, 4, 6) (2, 5, 8) (3, 7, 9)
3. (1, 4, 6) (2, 5, 7) (3, 8, 9)
4. (1, 2, 3) (4, 5, 6) (7, 8, 9)

Answer: The figures 1, 4 and 6 have two triangles, two circles and two hexagons, respectively. Figures 2, 5 and 8 are similar in shape. In figures 3, 7 and 9 there are eight small circles around a big circle. Now let us move on to more solved examples on the Grouping of Figures.

### Part D

Example 7: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: 1. (1, 5, 6) (2, 3, 4) (7, 8, 9)
2. (1, 2, 4) (3, 5, 8) (6, 7, 9)
3. (5, 6, 7) (1, 2, 4) (3, 8, 9)
4. (1, 2, 4) (3, 5, 7) (6, 8, 9)
5. none of the above

Answer: In the question figure we see that the figures that we label 1, 2 and 4 all consist of three lines. Also, the figures 3, 5 and 8 all consist of four lines each. Similarly, we can see that the figures 6, 7 and 9 all consist of five lines. Therefore this gives us the grouping of the figures. Thus the correct option is B.

Example 8: In the following question, group the given figures into three classes using each figure only once.

Problem Figure: 1. (1, 7, 8) (2, 6, 5) (3, 4, 9)
2. (1, 8, 9) (2, 3, 5) (4, 6, 7)
3. (2, 3, 5) (1, 7, 8) (4, 6, 9)
4. (2, 6, 7) (1, 3, 4) (5, 8, 9)
5. none of the above

Answer: As is clear from the question figure, the figures 2, 3 and 5 have one point or in other words, we can say that they are a one-pointed system. Also, we can see that the figures 1, 8 and 9 are made up of four lines. Below we have some practice problems on the Grouping of Figures.

## Problems For Practice

In the below question, a series of figures is given which can be grouped into classes. Select the group into which the figures can be classified from the given responses.          [S S C  (C P O) 2010]

Problem Figure 1. (146, 35, 278)
2. (258, 138, 46)
3. (37, 145, 258)
4. (258, 16, 47)
5. none of the above

Ans: A. (146, 35, 278)

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