# 5th Class Mathematics Reasoning and Aptitude Reasoning and Aptitude

## Reasoning and Aptitude

Category : 5th Class

Reasoning and Aptitude

Introduction

Learning process is dependent on ones ability to think logically and reason quickly and effectively. So Reasoning and logic skills are an important part in our progress as these skills are very useful in our day to day life. In this chapter, we will learn various problems related to reasoning and aptitude.

Problems Based on Patterns

Patterns is a list of numbers or letters that follows a certain sequence of a certain rule. To solve them all we have to do is figure out the pattern and come up with the next logical number or letter of the sequence.

•             Example

Which number will replace the question mark (?) in the number pattern given below?

(a) 18                                                                (b) 22

(c) 16                                                                (d) 14

(e) None of these

Explanation: Pattern followed in is $Q\,\,=\,\,\frac{P}{2}\,\,+\,\,2$

Or, $6\,\,=\,\,\frac{8}{2}\,\,+\,\,2=\,\,4\,\,+\,\,2,\,\,9\,\,=\,\,\frac{14}{2}\,\,+\,\,2\,\,=\,\,7\,\,+\,\,2,\,\,12\,\,=\,\,\frac{20}{2}\,\,+\,\,10\,\,+\,\,2$

So, $?\,=\,\frac{28}{2}+2=14+2=16.$ Hence, missing number is 16.

Figure Pattern

Figure pattern is a collection of figures that follows a certain sequence or a certain rule.

•              Example

How many squares will be there in pattern (31)?

(a) 103                                                              (b) 94

(c) 98                                                                (d) 89

(e) None of these

Explanation: Number of squares in Pattern $(1)\,\,=\,\,(3\,\times \,1)\,\,+\,\,1\,\,=\,\,4$

Number of squares in Pattern $(2)\,\,=\,\,(3\,\times \,2)\,\,+\,\,1\,\,=\,\,7$

Number of squares in Pattern $(3)\,\,=\,\,(3\,\times \,3)\,\,+\,\,1\,\,=\,\,10$

Number of squares in Pattern $(4)\,\,=\,\,(3\,\times \,4)\,\,+\,\,1\,\,=\,\,13$

Therefore, Number of squares in Pattern $(31)\,\,=\,\,(3\,\times \,31)\,\,+\,\,1\,\,=\,\,93\,\,+\,\,1\,\,=\,\,94$

Problems Based on Alphabet Test and Word Formation

Alphabet test is one of the most common topic of reasoning where we come across various types of problems as follows:

•              Example

Find out the which cannot be made from the letters of the given word.

PROGRAMMING

(a) Margin                                                          (b) Ranger

(c) Paring                                                           (d) Ingram

(e) None of these

Explanation: In the word ?Ranger? the letter ?E? is not in the given word PROGRAMMING.

•             Example

Arrange the given words as they are arranged in dictionary.

1. Excuse         2. Execute        3. Exclude        4. Exciting       5. Example

(a) 5, 4, 2, 3, 1                                                   (b) 5, 4, 3, 1, 2

(c) 5, 3, 4, 1, 2                                                   (d) 4, 5, 3, 1, 2

(e) None of these

Explanation: Correct order of the given words as arranged in dictionary is:

•                    Example

Find the next pair of letters in the series given below:

(a) LV                                                               (b) FV

(c) EU                                                               (d) BI

(e) None of these

Explanation: Pattern is as follow:

So, the required pair is FV.

•              Example

Which of the following letters is 9th to the left of 7th letter from the right end?

ABCDEFGHIJKLMNOPQRSTUVWXYZ

(a) M                                                                 (b) K

(c) L                                                                  (d) N

(e) None of these

Explanation: 7th alphabet from the right end is ?T? and 9th to the left of ?T? is ?K?.

•              Example

Identify the one that does not belong to the group.

(a) POS                                                             (b) QPR

(c) MLN                                                             (d) UTV

(e) FEG

Explanation: There are three consecutive letters in QPR, MLN, UTV and FEG but the letters in POS are not consecutive.

Problems Based on Analogy and Classification

Simple meaning of analogy is similarity. But in terms of reasoning, the meaning of analogy is logical similarity in two or more things. In analogy based problems, we will usually be given one pair of images that are connected in a particular way and the first image of a second pair. We have to find the correct image to complete the second pair in the same way as the first pair.

Classification of figures or shapes test our ability to work out which shapes are similar and which are different in a given set of options. We need to use our observation skill to compare given shapes, symbols and find the visual link or links.

•                    Example

Identify the relationship between the pair of figures given on either side of :: and then find the missing figure.

(a)                                              (b)

(c)                                             (d)

(e) None of these

Explanation: The upper figure is converted into a figure similar to the lower figures and each one of the lower figures is converted to a figures similar to the upper figure.

•              Example

Find the odd one out.

(a) $\frac{12}{L}$                                                                     (b) $\frac{9}{I}$

(c) $\frac{27}{Y}$                                                                     (d) $\frac{19}{S}$

(e) $\frac{13}{M}$

Explanation: Letters to the English alphabet and their positions are as follow:

A$\to$1, B$\to$2, C$\to$3, D$\to$4, ?????I $\to$9, ????? S $\to$19 ?????. Y $\to$

Therefore, the relation given in option (c) is the odd one out.

•             Example

Find the figure which is different from the rest.

(a)                                                             (b)

(c)                                                (d)

(e)

Explanation: Except the figure given in option (b), all other figures in options (a), (c), (d) and (e) have inner part shaded.

Problems Based on Geometrical Shapes

Geometrical shapes come from geometry which is the math of shapes made of points and lines. Some shapes are simple such as the triangle, square and circle, whereas and lines. Some shapes are simple such as the triangle, square and circle, whereas other shapes are complex. While solving logical reasoning based on geometrical shapes, following points are important:

·         Largest Perimeter: If the length of a figure does not change but width changes, then the figure having largest width have the largest width have the largest perimeter.

·         Net of Cube: Net is a pattern that we can cut and fold to make a model of a solid shape. A net of a cube have 6 faces and when folded, it form a box.

·         Net of Cuboid: Same as cube, it also has different types of net, depending upon that how you unfold it. It has also 6 faces in which pair of opposite faces are same.

·         Rotation: Turning of any figure around a point is called rotation.

(i)     Two half rotations mean one full rotation.

(ii)    $\frac{1}{4}$ rotation means figure rotates $90{}^\circ$anticlockwise.

(iii)   $\frac{1}{8}$ rotation means figure rotates $45{}^\circ$clockwise or $45{}^\circ$anticlockwise.

·         Counting Geometrical Shapes: In order to count the geometrical shapes, we identify the shapes and solids by their names and images.

·         Embedded: If a figure contains another figure as its parts, the figure part is called embedded figure.

•             Example

How many lines of symmetry does the given figure have?

(a) 0                                                                  (b) 1

(c) 2                                                                  (d) 4

(e) None of these

Explanation: The given figure has exactly one line of symmetry.

•             Example

For a cube how many cubes are there in the figure given below?

(a) 44                                                                (b) 48

(c) 46                                                                (d) 52

(e) None of these

Explanation: Number of cubes in first layer = 14

Number of cubes in second layer = 14

Number of cubes in third layer = 8

Number of cubes in fourth layer = 4

Number of cubes in fifth layer = 4

Total number of cubes = 14 + 14 + 8 + 4 + 4 = 44

•               Example

How many triangles are there in the figure given below?

(a) 8                                                                  (b) 10

(c) 12                                                                (d) 14

(e) None of these

Explanation: Clearly, there are 10 triangles in the given figure.

•              Example

Count the number of right angles inside the figure given below.

(a) 8                                                                  (b) 20

(c) 12                                                                (d) 16

(e) None of these

Explanation: There are 12 right angles in the figure inside the given figure.

Problems Based on Mirror Images and Water Images

Mirror Image

In a plane mirror, if we lift our right hand, the image in the mirror shows our left hand and if we lift our left hand, the image shows our right hand. Therefore, in a mirror image, the left part of an object becomes right part and the right part becomes left part.

Left hand Side (LHS)  Right Hand Side (RHS)

For example,

Water Image

A water image is an identical object but turned upside down (vertically inverted image). The position of the water layer is horizontally just below the object. In water image the Lower and Upper part interchange position and the Left and Right parts remains same.

For example,

•               Example

Find the mirror image of the given figure.

(a)                                               (b)

(c)                                                (d)

(e) None of these

Explanation: Mirror Image is as follow:

•              Example

Find the water image of the given figure.

............................... Water

(a)                     (b)

(c)                      (d)

(e) None of these

Explanation: Water Image is as follow:

........................ Water

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