PROBLEM SOLVING

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PROBLEM-SOLVING

 
 
 
In the domain of logical reasoning known as Problem Solving Reasoning, candidates encounter a range of questions that necessitate the application of various operations, including addition, division, greater than, lesser than, and others, which may be interchanged or substituted to determine the correct answers. This section is commonly featured in government examinations, covering topics such as Inequality, Analogy, Series, Puzzle, and more
 
What is Problem Solving Reasoning?
 

Problem Solving Reasoning refers to a logical reasoning component often found in various competitive exams and assessments. In this section, candidates are presented with a series of questions that require logical thinking and analytical skills to arrive at the correct solutions. The questions typically involve manipulating or interchanging various elements, such as numbers, symbols, or operations, to deduce the answer.

Key characteristics of Problem Solving Reasoning include:

  • Logical Operations: Candidates are required to perform logical operations, such as addition, subtraction, multiplication, division, and comparisons (greater than, lesser than), on given elements.

  • Substitution or Interchange: The questions often involve the substitution or interchange of elements within a given context. This challenges candidates to identify the appropriate substitutions or changes to arrive at the correct answers.

  • Common Topics: The section covers a range of topics, including but not limited to Inequality, Analogy, Series, Puzzles, and other logical patterns.

  • Application in Examinations: Problem Solving Reasoning is a common component in government examinations and various competitive tests. It assesses a candidate's ability to approach and solve problems using logical reasoning skills

 
Inequality in reasoning with all the symbols
 

inequalities involve expressing relationships between two quantities or expressions using symbols that represent their relative magnitudes. The common inequality symbols are:

  1. Greater Than: >

    • Example: 5>3 indicates that 5 is greater than 3.
  2. Less Than: <

    • Example: 2<7 indicates that 2 is less than 7.
  3. Greater Than or Equal To:

    • Example: 4≥4 indicates that 4 is greater than or equal to 4.
  4. Less Than or Equal To:

    • Example: 9≤10 indicates that 9 is less than or equal to 10.
  5. Equal To: =

    • Example: 6=6 indicates that 6 is equal to 6.
  6. Not Equal To:

    • Example: 3≠7 indicates that 3 is not equal to 7.
 
Inequality Symbol Meaning Example
> Greater Than 5>3 (5 is greater than 3)
< Less Than 2<7 (2 is less than 7)
Greater Than or Equal To 4≥4 (4 is greater than or equal to 4)
Less Than or Equal To 9≤10 (9 is less than or equal to 10)
= Equal To 6=6 (6 is equal to 6)
Not Equal To 3≠7 (3 is not equal to 7)
 
Exams where Problem Solving Reasoning is Part of Syllabus
 

Problem Solving Reasoning is an integral part of the syllabus in various competitive exams and standardized tests. It is included to assess candidates' logical thinking, analytical abilities, and problem-solving skills. Here are some exams where Problem Solving Reasoning is commonly found in the syllabus:

  • UPSC Civil Services Examination (CSAT): The Civil Services Aptitude Test (CSAT) includes a problem-solving reasoning section to evaluate candidates' decision-making and analytical skills.

  • SSC (Staff Selection Commission) Exams: Exams conducted by SSC, such as SSC CGL (Combined Graduate Level), SSC CHSL (Combined Higher Secondary Level), and others, include reasoning sections covering problem-solving skills.

  • Bank Exams: Banking exams like IBPS PO, SBI PO, and other clerical exams have reasoning sections that often include problem-solving reasoning questions.

  • Railway Recruitment Exams: Examinations conducted by Railway Recruitment Boards (RRBs) for various positions often have reasoning sections that involve problem-solving reasoning.

  • CAT (Common Admission Test): CAT, a prerequisite for admission to many Indian Institutes of Management (IIMs) and other prestigious management institutes, includes a section on Data Interpretation and Logical Reasoning (DILR), which encompasses problem-solving reasoning.

  • GRE (Graduate Record Examination): The GRE includes sections like Analytical Writing and Verbal Reasoning that assess candidates' problem-solving and reasoning abilities.

  • GMAT (Graduate Management Admission Test): GMAT includes a section on Integrated Reasoning that assesses candidates' ability to analyze and solve complex problems.

  • CLAT (Common Law Admission Test): CLAT, an entrance exam for admission to law schools, includes a section on Legal Reasoning that involves problem-solving scenarios.

  • CAT (Common Admission Test) - USA: CAT, administered by the American Psychological Association (APA), assesses cognitive abilities and includes a problem-solving section.

  • MAT (Management Aptitude Test): MAT is used for admission to various management programs and includes sections that evaluate candidates' analytical and problem-solving skills

 
 
 
Solved Examples of Problem Solving
 

 

Example 1:

Problem: In a certain code language, "APPLE" is written as "MMPRF." How is "ORANGE" written in that code?

Solution: In the given code, each letter is replaced by the letter that comes four places later in the English alphabet.

  • A + 4 = M
  • P + 4 = M
  • P + 4 = P
  • L + 4 = R
  • E + 4 = F

Applying the same logic to "ORANGE":

  • O + 4 = S
  • R + 4 = V
  • A + 4 = E
  • N + 4 = R
  • G + 4 = K
  • E + 4 = I

Therefore, "ORANGE" is written as "SVEIRK" in that code.

 

Example 2:

Problem: There are six friends - Alex, Ben, Chris, Dana, Evan, and Fiona. They each have a different favorite color: Red, Blue, Green, Yellow, Purple, and Orange.

  1. Chris's favorite color is not Red or Blue.
  2. Evan's favorite color is Yellow.
  3. Fiona's favorite color is not Purple or Orange.
  4. Ben's favorite color is not Green or Red.
  5. Dana's favorite color is not Green.

What is each person's favorite color?

Solution:

  • Evan's favorite color is Yellow.
  • Since Dana's favorite color is not Green, Dana's favorite color must be Red.
  • From the information given, Ben's favorite color is Blue (it cannot be Green or Red).
  • Now, we know the favorite colors of Evan, Dana, and Ben. Let's fill in the remaining colors for Chris, Fiona, and Alex:
    • Chris's favorite color is Green (it cannot be Red or Blue).
    • Fiona's favorite color is Orange (it cannot be Purple or Orange).
    • Alex's favorite color is Purple (the only color left).

Therefore, the favorite colors are:

  • Alex: Purple
  • Ben: Blue
  • Chris: Green
  • Dana: Red
  • Evan: Yellow
  • Fiona: Orange

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