Paper I: General Intelligence and Reasoning

Topic: Relationship Concepts, Arithmetical Reasoning, and Figure Classification

1. Relationship Concepts

Relationship concepts in reasoning are all about understanding how different entities, people, or objects are connected to each other. These connections can be based on blood relations, professional roles, social interactions, or even abstract associations. The key to solving these problems is to carefully analyze the given information and deduce the specific link being asked.

1.1 Blood Relations

Blood relation problems are very common. They involve understanding family ties like parents, siblings, children, uncles, aunts, cousins, grandparents, and in-laws. To solve these, it's often helpful to draw a family tree or use symbols to represent genders and relationships.

Example: Pointing to a photograph, a man said, "I have no brother or sister, but that man's father is my father's son." How is the man in the photograph related to the man who is speaking?

Explanation: 'My father's son' refers to the speaker himself, as he has no brother. So, the statement becomes, "That man's father is me." Therefore, the man in the photograph is the speaker's son.

1.2 Professional and Social Relationships

These problems involve relationships based on jobs, roles, or social connections. For instance, a doctor and a patient, a teacher and a student, a boss and an employee, or friends. The logic is similar to blood relations: understand the roles and how they connect.

Example: A is B's sister. C is B's mother. D is C's father. E is A's son. How is D related to A?

Explanation: A is B's sister. C is B's mother. So, C is also A's mother. D is C's father. This makes D the maternal grandfather of A.

2. Arithmetical Reasoning

Arithmetical reasoning tests your ability to solve problems using basic mathematical operations and logical deduction. These problems often appear as word problems, requiring you to translate the text into mathematical equations or logical steps. They test your understanding of numbers, ratios, percentages, averages, and basic algebra.

2.1 Age Problems

These problems involve calculating ages based on given conditions, such as the ratio of ages at different times, or the difference in ages.

Example: The sum of the ages of a father and son is 60 years. Six years ago, the father's age was five times the son's age. Find their present ages.

Explanation: Let the present age of the father be F and the son be S. Given: F + S = 60 (Equation 1) Six years ago, father's age was (F-6) and son's age was (S-6). Given: F - 6 = 5 * (S - 6) F - 6 = 5S - 30 F = 5S - 24 (Equation 2) Substitute Equation 2 into Equation 1: (5S - 24) + S = 60 6S = 84 S = 14 years Now find F using Equation 1: F + 14 = 60 F = 46 years So, the father is 46 years old and the son is 14 years old.

2.2 Ratio and Proportion Problems

These problems involve finding unknown quantities when given ratios or proportions between them.

Example: The ratio of two numbers is 3:7. If the sum of the numbers is 110, find the numbers.

Explanation: Let the numbers be 3x and 7x. Given: 3x + 7x = 110 10x = 110 x = 11 The numbers are 3 * 11 = 33 and 7 * 11 = 77.

2.3 Percentage and Profit/Loss Problems

These require calculating percentages, discounts, profit margins, and loss percentages.

Example: A shopkeeper buys an article for ₹400 and sells it for ₹480. What is his profit percentage?

Explanation: Cost Price (CP) = ₹400 Selling Price (SP) = ₹480 Profit = SP - CP = 480 - 400 = ₹80 Profit Percentage = (Profit / CP) * 100 Profit Percentage = (80 / 400) * 100 = (1/5) * 100 = 20%

2.4 Average Problems

These problems involve calculating the average of a set of numbers or finding a missing number given the average.

Example: The average of 5 numbers is 20. If one number is removed, the average becomes 18. What is the removed number?

Explanation: Sum of 5 numbers = Average * Number of items = 20 * 5 = 100 Sum of the remaining 4 numbers = Average * Number of items = 18 * 4 = 72 The removed number = (Sum of 5 numbers) - (Sum of 4 numbers) = 100 - 72 = 28.

3. Figure Classification

Figure classification, also known as non-verbal reasoning, involves analyzing a set of figures (shapes, patterns, or objects) and identifying the one that does not belong with the others, or grouping figures based on a common characteristic. This tests your visual perception, analytical skills, and ability to identify patterns and differences.

3.1 Identifying the Odd One Out

In this type of question, you are given a set of figures, and you need to select the figure that is different from the rest based on some logical criterion. The criteria can be varied:

• Number of sides/angles
• Presence or absence of specific elements (e.g., dots, lines, curves)
• Symmetry
• Rotation or reflection
• Internal or external elements
• Shading patterns
• Connectivity of lines
• Shape progression

Example: Which figure does not belong with the others? (Imagine four figures here: a square, a circle, a triangle, and a rectangle)

Explanation: In this case, the circle is the odd one out because it is a curved shape, while the square, triangle, and rectangle are all polygons with straight sides and angles.

Another Example: (Imagine four figures: Figure 1 has a square with a diagonal line. Figure 2 has a circle with a horizontal line. Figure 3 has a triangle with a vertical line. Figure 4 has a pentagon with a line from one vertex to the center.)

Explanation: Figure 4 is the odd one out. In Figures 1, 2, and 3, the line drawn inside is a simple line segment (diagonal, horizontal, vertical). In Figure 4, the line is drawn from a vertex to the center, which is a different kind of internal division. Alternatively, if the criterion is the type of shape, and Figures 1, 2, and 3 are simpler shapes (4, 3, 3 sides respectively), while Figure 4 is a pentagon (5 sides), it could also be the reason. Always look for the most consistent logical difference.

3.2 Grouping of Figures

Here, you are given a set of figures, and you need to group them into the minimum number of categories, where all figures in a category share a common characteristic.

Example: (Imagine 9 figures: 3 simple triangles, 3 squares, 3 circles. Within each shape, there are variations like shading, internal lines, or dots.)

Explanation: The most straightforward grouping would be: Group 1: All triangles Group 2: All squares Group 3: All circles Other possible groupings could be based on internal features like shading or dots, but the shape itself is usually the primary classification.

4. Interrelation of Concepts

Often, these categories are combined. For instance, you might encounter a relationship problem that requires basic arithmetic, or a figure classification problem where the relationship between elements within the figure is key. Understanding each concept individually makes it easier to tackle combined problems.

Example combining Relationship and Figure: Consider a figure with two interlocking rings. If the problem states that the rings represent two different groups (e.g., 'Students' and 'Players'), and the overlapping section represents 'Students who are also Players', you need to use your understanding of sets and relationships to answer questions about the number of students, players, or both.

Example combining Arithmetical Reasoning and Figures: A grid of squares is given. Some squares are shaded. The problem might ask you to calculate the percentage of shaded squares or the ratio of shaded to unshaded squares. This requires counting and basic arithmetic applied to a visual representation.

Consistent practice with diverse examples from each category will build confidence and speed, essential for excelling in competitive exams.