Consider the following figures: 
What is the missing number?
UPSC - 2011
To solve this problem, we need to identify the pattern used in the first figure and apply it to the second figure to find the missing number.
Correct Option: C) 9
Consider the following figure and answer the item that follows: 
A square is divided into four rectangles as shown above. The lengths of the sides of rectangles are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square?
UPSC - 2011
10
11
15
Cannot be determined as the given data are insufficient
The problem involves a square divided into four rectangles, with given areas for two of them. We need to determine the length of each side of the square using these areas.
Correct Option: B) 11
Examine the following statements:
1. None but students are member+B4s are member of the club.
2. Some members of the club are married persons.
3. All married persons are invited for dance.
Which one of the following conclusions can be drawn from the above statements?
UPSC - 2012
All students are invited for dance.
All married students of the club are invited for dance.
All members of the club are married persons.
None of the above conclusions can be drawn.
This problem involves deductive reasoning based on a series of categorical statements. We need to analyze each statement and combine the information to find a conclusion that logically follows. We can use Venn diagrams or logical deduction to represent the relationships between different groups of people.
B) All married students of the club are invited for dance. This conclusion directly follows from combining the statements. Statement 2 establishes the existence of "married members of the club" (who are also students). Statement 3 states that all married persons are invited for dance. Therefore, these specific married members (who are students) must also be invited for dance.
Directions for the following 3 items given below (Questions 4-6)
Out of four friends A, B, C and D,
A and B play football and cricket,
B and C play cricket and hockey,
A and D play basketball and football,
C and D play hockey and basketball.
Who does not play hockey?
UPSC - 2013
The problem requires identifying which friend does not play hockey based on the given information about who plays which sports. We will list the sports played by each person and then check who does not have 'hockey' in their list.
From the consolidated list, Friend A's sports are football, cricket, and basketball. Hockey is not listed for Friend A.
D) A is the correct answer because Friend A plays football, cricket, and basketball, but not hockey.
Who plays football, basketball and hockey?
UPSC - 2013
This question asks to identify the person who plays all three sports: football, basketball, and hockey. This is a Venn diagram-based problem, where each circle represents a sport and the overlapping regions represent players who play multiple sports. We need to find the region that is common to all three circles.
A) D is the correct answer because, in a typical Venn diagram representing three categories (Football, Basketball, and Hockey), the letter 'D' is positioned in the central area where all three circles overlap. This signifies that 'D' represents the individual who plays all three sports.
Which game do B, C and D play?
UPSC - 2013
The question asks to identify the game played by individuals B, C, and D. This is a logical reasoning question that requires interpreting a given statement or context, which is missing in the provided prompt. However, based on the correct answer provided (Hockey), the question likely refers to a specific context or a diagram that was part of the original UPSC 2013 paper. Without that context, we must assume the question is based on general knowledge or a previously established scenario.
Since the original context (like a diagram or a passage describing the players and their games) is not provided, we must rely on the given correct answer to infer the scenario. In competitive exams, such questions often come with a visual representation (e.g., a Venn diagram, a table, or a picture) or a textual description. Assuming such a context existed and indicated that B, C, and D are associated with Hockey, the answer would be B.
For a question like this in an actual exam, one would typically:
Without the source material, a definitive step-by-step derivation is not possible. However, given the correct answer is Hockey, we proceed with that assumption.
B) Hockey
Assuming the original question included a context (e.g., a diagram or a passage) that showed B, C, and D are participants in the game of Hockey, then Hockey would be the correct answer. This type of question tests the ability to extract specific information from a given data set or visual representation.
The incorrect options are simply other sports that would not be the answer if the information in the original question (which is not provided) pointed to Hockey for players B, C, and D.
