**Shortcuts in Reasoning for Competitive Exams – Visual Reasoning**

Shortcuts in Reasoning Quantitative Aptitude English

#### Visual Reasoning

**INTRODUCTION**

Visual intelligence measures the ability to process visual material and to employ both physical and mental images in thinking. As a result people with a high visualization find it easier to comprehend information and communicate it to others. Your visualization skills determine how well you perceive visual patterns and extract information for further use. Visualization also facilitates the ability to form associations between pieces of information something which helps improve long term memory.

**Types of Visual Reasoning**

Odd-Man Out Type

Counting of Figures

**I . ODD-MAN OUT TYPE**

**1. Rotation of same Figure**

This is the most common type of classification. The similar figures are actually the rotated forms of the same figure in clockwise or anti-clockwise direction. The figure which comes out to be different from other is that figure which cannot be obtained by rotation of either of the other figures,

**EXAMPLE 1.**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different from other. Find the odd figure out.

**Solution .** After examining the above figure, it is found that except (d) all figures can easily be obtained by clockwise and anti-clockwise movement or each other.

**2. Number of Elements or Lines**

A group of figure maybe classified on the basis of number of elements or the number of lines present in figures. The figures can also be classified on even or odd number of lines or elements present in figures. Classification can also be done on the ratio of number of lines and elements.

**EXAMPLE 2**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different from other. Find the odd figure out.

**Solution .** All except figure (c) contains odd number of arrows.

**3. Division of Figures**

This type of classification is done on the equal or inequal division of figures or divisioin of figure in some specified ratio or parts.

**EXAMPLE 3.**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different

from other. Find the odd figure out.

**Solution .** Except figure (a) all figures are divided into two equal parts.

**4. Similarity of Figures**

Classification on the basis of similarity of figure is done when orientation, shape, measure of angle or method of presentation of group is same except for the odd figure.

**EXAMPLE 4.**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different from other. Find the odd figure out.

**Solution .** Let us consider the two adjacent bent lines as a pair. Then, in each figure except (d) there are two straight lines between the bent pair and the remaining bent line when the direction of bent is considered.

**5. Relation between Elements of Figure**

In this type of classification, the elements of the figure bears a certain relationship between them in which the odd figure does not posses. This relation can be based on shape of elements presents, inversion of elements etc.

**EXAMPLE 5.**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different

from other. Find the odd figure out.

**Solution .** Except figure (c) in all the figures, both the inside and outside figures are similar but differ in size.

**6. Interior-Exterior Consideration of Elements**

A figure can be formed from two or more elements, it is likely that some elements may lie in interior of other elements while some may lie in the exterior of the other elements. This consideration can be used for classification of elements from a group.

**EXAMPLE 6.**

**Directions :** In the following question, a group of five figures is given. Out of which four figures are similar to each other in a certain way and one is different from other. Find the odd figure out.

**Solution .** Only figure (d) does not contain any element present in the interior of the closed figure.

**II . COUNTING OF FIGURES TYPE**

**Type-1 :** Counting of Straight Lines and Triangles

**(a) Straight lines**

**Shortcut Approach**

Then, on counting, it will be counted as one line, i.e., AB and not as a two straight lines AC and CB

**EXAMPLE 1.**

How many straight lines are there in the figure ?

**Solution .**

Horizontal lines=AB+PQ + DC=3

Vertical lines = AD + RS + BC = 3

Slant lines = 0

Total lines = 3+ 3+ 0 = 6

**(b) Triangle –** it is a closed figure bounded by three side.

**Shortcut Approach**

- Smallest triangles are counted first.
- Now, counted those triangles which are formed with the two triangles and further counting goes on in the same way.
- Largest triangle is counted in the last

**EXAMPLE 2 .**

How many triangles are there in the figure?

**Solution .**

**Type-2 :** Counting of Quadrilaterals and Polygons

**Square**

It has four equal sides, equal diagonals, and each of the four angles equal to 90°.

**Shortcut Approach**

- Count smallest squares first.
- Now, count squares which are formed with two squares andi further counting goes on in the same way.
- Largest square is counted in the last.

**EXAMPLE 3 .**

How many square are there in the figure ?

**Solution .**

**Formula for Counting Squares**

Let r be the number of rows and c be the number of columns.

Now, total number of squares = (r x c) + {(r -1 ) x (c – 1 ) + (r – 2) x (c – 2) + ………….

The terms are continued upto the term which is equal to zero (0). This method is applicable only to the figure, where each row and column is divided into squares of equal sections.

**Rectangle**

It has four sides, and opposite

sides are equal. It has equal

diagonals and each of the four

angles is equal to 90°.

**EXAMPLE 4.**

How many rectangles are there in the figure ?

**Solution .**

Formula for Counting of Rectangles and Parallelograms

Let r be the number of rows and c be the number of columns.Now, total number of rectangles or parallelograms

= [(r+(r-l) + (r-2) + +1]

x [c+ (c – l) + (c-2)+ + 1]

The method is applicable only to the figure, where each row and column is divided into rectangle of equal sections.

**Type-3 : Circle**

Circle is a closed figure. It has zero sides.

**Shortcut Approach**

- Keep writing numbers one by one inside the circles starting from i.e., for 1st circle put 1, for 2nd circle put 2, for 3rd circle put 3 and so on.
- The number which is put for the last circle is the required number of circles.

**EXAMPLE 5.**

How many circles are there in the figure ?

**Solution .** Here, we start counting of circles and mark them, as 1, 2 and so on and finally we end on getting 5 number of circles as shown below:

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