Reasoning: 2 Types of Inequality Problems

Dear Reader, in this tutorial you will find two kinds of inequality problems. These are easy to score, but many fail due to lack of preparation. Hence learn the below examples thoroughly and stay prepared.

At the end of this tutorial, you will find a short practice test.

Type 1: Interpretation of Expression

In type 1, you have to interpret a given expression. Then you have to find which option satisfies the expression. Below is an example.

Example Question 1: Which of the following expression will be true if the expression P>Q=R<S is definitely true?
a) P > R b) P = R c) P > S d) Q > S
Reason:
The given expression is,
P > Q = R < S
Here Q and R are equal.
So if P is greater than Q, then P will also be greater than R. Hence option a is true.

Type 2: Symbol Mapping

In the question, you will find symbols and their meanings. You have to replace the symbols with their signs to form an expression. Based on the expression you have to answer the following questions.

Example Question 2: In the following question, the symbols , §, =,*,δ are used with the following meanings:
‘’ means ‘P is greater than Q’;
‘P§Q’ means ‘p is greater than or equal to Q’;
‘P=Q’ means ‘P is equal to Q’;
‘P*Q’ means ‘P is smaller than Q’;
‘PδQ’ means ‘P is smaller than or equal to Q’;
Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I or II is/are definitely true.
Give answer (a) if only conclusion I is true;
Give answer (b) if only conclusion II is true;
Give answer (c) if either conclusion I or II is true;
Give answer (d) if neither conclusion I or II is true;
Give answer (e) if both conclusion I and II is true;

1. Statements:
S*M, , L§Z
Conclusions:
1. S=Z 2. SδL
Options: a, b, c, d, e
Answer: d) neither conclusion I or II is true
Reason:
Given Statements are S*M, , L§Z

We can convert the statements as follows:
S*M – S is smaller than M (i.e.) S<M;
– M is greater than L (i.e.) M>L;
L§Z – L is greater than or equal to Z (i.e.) L≥Z;
Combining the above we get the expression:
S<M>L≥Z

Now we have to check the given conclusions with the expression we got above.
Given conclusions are:
1. S=Z 2.S*L (i.e.) S≤L
We cannot compare S and Z. So conclusion I is not true
Similarly, S and L also cannot be compared. So conclusion II is also false
Hence, neither conclusion I nor II is true.

2. Statements:
J=V, V*N, RδJ
Conclusions:
1. R*N 2. J§N
Options: a, b, c, d, e
Answer: a) only conclusion I is true
Reason:
Given statements are J=V, V*N, RδJ
We can convert the statement as follows:
J=V – J is equal to V;
V*N – V is smaller than N (i.e.) V<N
RδJ – R is smaller than or equal to J (i.e.) R≤J
Combining the above, we get the expression:
J = V < N, R ≤ J
i.e., R ≤ J = V < N

Given conclusions are:
1. R*N (i.e.) R<N 2. J§N (i.e.) J≥N
As per the equation R≤J = V<N
R<N is true (i.e.) conclusion I is true

From our expression we can write J = V < N. Because J=V, J should also be lesser than N.
Therefore, J < N.
But our conclusion says, J≥N.
So conclusion II is false.
Hence conclusion I is true.