Maths Inequalities Questions with Answers

Types of Inequalities Questions 

In banking exams, the reasoning section comprises various types of inequalities questions to assess a candidate's ability to analyze and establish relationships between different elements. Let's introduce you to the different types of Inequalities questions you may encounter in your exams:

a) Single Statement Inequalities: In single statement inequalities, the relationships between elements are conveyed through a series of coded symbols, which include '<,' '>,' '=,' '≤,' or '≥.' This forms the foundation of Inequalities questions and tests your fundamental understanding of relationships.

For example; X > K = L ≥ M ≥ Y > Z
Conclusion:

I. Z > M (false)
II. L < X (true)

b) Multiple Statements Inequalities: In multiple statements inequalities, relationships between elements are presented in two or more distinct series. To determine the precise relations, the task involves organizing and aligning similar elements into a unified series.

For example
L > R < V
K > J = L

To establish the definite relations, first we have to arrange the elements into a single series:
K > J = L > R < V

To establish the definite relations, first we have to arrange the elements into a single series:
K > J = L > R < V

(C) Missing Inequalities:  In this type of question, the relationships between elements are not explicitly provided. Instead of coded symbols (<, >, =, ≤, ≥, ≠), blanks or spaces are presented. Your task is to deduce and fill in the appropriate coded symbols based on specific conditions typically mentioned in the questions.

For example:
Q. Which of the following order of letters (from left to right) in the blanks makes the expression, M > S definitely true?
____ = ____ > ____ ≤ ____ = ____
1) B, G, M, T, S
2) S, M, T, G, B
3) M, B, S, T, G
4) T, S, G, B, M
5) None

Correct Answer: c) M, B, S, T, G
In this order, the expression becomes:
M = B > S ≤ T = G
And, as per the question, M is definitely greater than S (M > S).

(d) Coded Inequalities: Coded inequalities involve multiple statements with logical and arithmetic relationships between them. In this type of question, Inequalities symbols are assigned specific codes in the form of special symbols. You'll be given expressions where these codes are used, and your task is to decode these symbols to discern the relationship between the elements in the expression. These statements are followed by a set of conclusions, and your task is to determine which conclusion is consistent with the given statements.

For example: In the following statements, some symbols are given with decoded meanings as follows

1. ‘A @ B’ means ‘A is neither greater than nor smaller than B.’
2. ‘A % B’ means ‘A is not greater than B.’
3. ‘A # B’ means ‘A is neither smaller than nor equal to B.’
4. ‘A © B’ means ‘A is not smaller than B.’
5. ‘A δ B’ means ‘A is neither greater than nor equal to B.’

Statements:     J # K, K @ P, P δ R
Conclusions:    I. J # R     II. R δ J

J # K means J > K
K @ P means K = P
P δ R means P < R

So, the final equation will be, J  >  K  =  P  <  R
Now you can solve it accordingly.

Solving Inequalities: Tips and tricks

Each of these types of Inequalities based question poses its unique challenges and demands a particular set of skills. A strong grasp of these various Inequalities question types, along with regular practice, will prepare you to tackle this section effectively in banking exams, ultimately contributing to your overall success. Here are some tips and tricks for solving inequalities:

• Transitive Property: When you encounter a sequence like A < B < C in a question, remember that the transitive property holds. This means that not only is A < B and B < C true, but you can also conclude that A < C. This simplifies the relationships and helps you draw quicker conclusions.
• Mixed Relations: When you have a combination like A > B ≥ C, focus on the most significant relationship. In this case, A > C is true, and you can disregard the B ≥ C part. Simplify the Inequalities by considering the stronger relationship.
• Equality and Inequalities: If you come across an expression like A ≥ B = C, remember that this means either A > C or A = C is true. In other words, if two elements are equal to a third element, they can either be greater than it or equal to it.
• Opposite Symbols: When you have a situation like A < B > C with opposite symbols, you cannot establish any direct relationship between A and C. In such cases, no conclusion can be drawn because the symbols contradict each other.

Even though inequalities seem simple, it's crucial to get your fundamentals right before tackling this topic in your exam to save yourselves from some obvious mistakes. For instance, if you see an inequality like A ≤ B = C, you can't immediately assume that A < C. It might seem true at first, but this assumption can lead to incorrect answers. In this case, A is either less than or equal to C, and we can't make a definite statement.

Even though inequalities seem simple, it's crucial to get your fundamentals right before tackling this topic in your exam to save yourselves from some obvious mistakes. For instance, if you see an inequality like A ≤ B = C, you can't immediately assume that A < C. It might seem true at first, but this assumption can lead to incorrect answers. In this case, A is either less than or equal to C, and we can't make a definite statement.