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Inequality PDF Set 1
Inequalities Quiz
Inequalities denote the relative size of two values. It is not only about equals in Maths, sometimes something is greater or less than.
Example: A and B have a race and B wins!
So, what do we know?
We don’t know how fast they ran, but we know that B ran faster than A.
So, we can write it down like this:
B > A
(Where B denotes how fast was B, ‘ > ’ denotes greater than and A denotes how fast A was)
We call the example, given above as inequalities as they are ’not equal’.
In the case of Inequalities, we need to be aware of the signs which include ( >, ≥, <, ≤ and = ). In such problems, the operator ‘ > ’ and ‘ < ‘ are accorded the highest priority. It is followed by ‘ ≥ ‘ and ‘ ≤ ‘.
On the other hand, ‘ = ‘ has the least priority.
So, if a statement is given as A > B ≥ C = D
Then A > C, D as ‘ > ’ has the highest priority.
B ≥ D as, ‘ ≥ ‘ has more priority than ‘ = ‘
Example:
Directions: In these questions, relationship between different elements is shown in the statement. The statement is followed by two conclusions. Choose the correct answer on the basis of information given below.
(1)
Statements: B > A ≥ T > F = Y ≤ S < D
Conclusions: F < D , A > S
A. Only conclusion I follows
B. Either conclusion I or conclusion II follows
C. Only conclusion II follows
D. Both conclusions follow
E. Neither conclusion I nor conclusion II follows
Ans. A
Statements: B > A ≥ T > F = Y ≤ S < D
Conclusions: F < D , A > S
For conclusion I: F < D
Here, the common sign between F and D is '<', hence F < D.
Thus conclusion I follows.
For conclusion II: A > S
Here, we can see the opposite sign between A and S, thus no relationship can be established between them.
Thus conclusion II does not follow.
Therefore only conclusion I follows.
Hence option A is correct.
(2)
Statements: Y < O ≤ G ≤ K = U > L > P
Conclusions: O = U , U > O
A. Only conclusion I follows
B. Either conclusion I or conclusion II follows
C. Only conclusion II follows
D. Both conclusions follow
E. Neither conclusion I nor conclusion II follows
Ans. B
Statements: Y < O ≤ G ≤ K = U > L > P
Conclusions: O = U , U > O
Here, the common sign between O and U is '≤', hence O ≤ U.
Thus, either O < U or O = U.
Therefore either conclusion I or II follows.
Hence option B is correct.
(3)
Statements : M < T < G ≤ J = U > Y > R
Conclusions : G < U , J > R
A. Only conclusion I follows
B. Either conclusion I or conclusion II follows
C. Only conclusion II follows
D. Both conclusions follow
E. Neither conclusion I nor conclusion II follows
Ans. C
Statements: M < T < G ≤ J = U > Y > R
Conclusions: G < U , J > R
Here, the common sign between G and U is '≤', hence G < U does not follow.
Therefore conslusion I does not follow.
And, the common sign between J and R is '>', thus J > R follows.
Therefore conclusion II follows.
Hence option C is correct.
(4)
Statement : 3 ≥ 9 < 7 ≤ 10 = 2 ≤ 6
Conclusions : I. 6 > 9 II. 9 ≤ 2
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or conclusion II follows
D. Both conclusions follow
E. Neither conclusion I or conclusion II follows
Ans. A
Statement: 3 ≥ 9 < 7 ≤ 10 = 2 ≤ 6
Conclusions: I. 6 > 9 II. 9 ≤ 2
Checking conclusion I: 6 > 9
From the given statement, we get:
While moving from 6 towards 9, the common sign of inequalities is '>' and the given conclusions is also '6 > 9'. Clearly, C1 follows.
Checking conclusion II: 9 ≤ 2
In the statement 9 < 7 ≤ 10 = 2, the common sign of inequalities between 9 and 2 is '<' whereas the given conclusion is '9 ≤ 2'. Therefore, C2 doesn't follow.
Option A is hence the correct answer.
Exams where Inequalities would appear include:
• SBI PO
• SBI Clerk
• SBI SO
• IBPS PO
• IBPS RRB
• IBPS CLERK
• IBPS SO
• SSC CGL
• NICL AO
• LIC AAO
Inequality is one of the topics where you can score full marks within a few minutes, thus saving on your precious time. It is expected that around 3 to 5 questions of Inequality appear in every competitive exam like IBPS PO, SBI PO, RRB PO etc.
Prior to moving forward, one needs to remember the following table:
Symbol  Meaning 
>  First element is greater than second element 
<  First element is smaller than second element 
=  First element is equal to second element 
≥  First element is greater than or equal to second element 
≤  First element is smaller than or equal to second element 
≠  First element is not equal to second element 
Understanding the priority of symbols
1. > / ≥ / =
Example:
B > P ≥ M = O
It would result in the following:
B > P, B > M, B > O, P ≥ M, P ≥ O and M = O
2. < ≤ =
Example:
P < X ≤ V = Y
It would result in the following:
P < Y, P < V, X ≤ V, X ≤ Y
3. > <
Example:
Q > K < M
It would result in the following:
No relation between Q and M.
4. > ≤
Example:
O > J ≤ H
It would result in the following:
No relation between O and H.
5. < >
Example:
F < E > Q
It would result in the following:
No relation between F and Q.
6. < ≥
Example:
D < S ≥ Z
It would result in the following:
No relation between D and Z.
The case of either  Or:
This is a special case and many times is a cause of confusion among candidates
Let us look at the conditions where ‘eitheror’ is applicable:
1) Both the conclusions should be wrong
2) Variables of both conclusions should be the same
Example:
Statement: P ≥ Q = R
Conclusion: (a) P > R (b) P = R
Here, both the options i.e a and b are false and both the variables (P, R) are the same. Thus, by combining both the conclusions the actual relationship between P and R is established.
So the correct answer would be to combine both signs given in the option i.e (P ≥ R)
Example:
Statement: H ≥ M ≤ V = K
Conclusions: (1) H < K (2) H ≥ K
Here, both the conclusion 1 and 2 are false and we cannot find the relation between H and K. The number of possibilities between H and K is
i.e. (a) H > K (b) H < K (c) H = K
So, this also a case of ‘eitheror’ as we are getting all possibilities by combining the conclusions.
Case of Coded Inequalities
Coded inequalities are the advanced format of the inequality questions. To solve them, one must be thorough with the signs, as discussed above.
Directions: Study the following information carefully and answer the questions given below.
‘A © B’ means ‘A is either smaller than or equal to B.’
‘A % B’ means ‘A is neither smaller than nor equal to B.’
‘A @ B’ means ‘A is either greater than or equal to B.’
‘A $ B’ means ‘A is neither greater than nor equal to B.’
‘A # B’ means ‘A is neither greater than nor smaller than B.’
(1)
Statements: P © R, R # F, F @ T
Conclusions: I. T © R II. F # P
A. if only conclusion I is true
B. if only conclusion II is true
C. if either conclusion I or II is true
D. if neither conclusion I nor II is true
E. if both conclusions I and II are true
Ans. A
As per the information given,
1. P © R means P ≤ R
2. R # F means R = F
3. F @ T means F ≥ T
So, the final equation will be,
P ≤ R = F ≥ T
Now, the Conclusion I. T © R means T ≤ R
the Conclusion II. F # P means F = P
Let's check the Conclusions now,
Conclusion I:
Conclusion II:
Hence, only Conclusion I is true.
(2)
Statements: L @ R, R % T, T # M
Conclusions: I. M $ R II. T $ L
A. if only conclusion I is true
B. if only conclusion II is true
C. if either conclusion I or II is true
D. if neither conclusion I nor II is true
E. if both conclusions I and II are true
Ans. E
As per the information given,
1. L @ R means L ≥ R
2. R % T means R > T
3. T # M means T = M
So, the final equation will be,
L ≥ R > T = M
Now, the Conclusion I. M $ R means M < R
the Conclusion II. T $ L means T < L
Let's check the Conclusions now,
Conclusion I:
Conclusion II:
Hence, both Conclusions I and II are true.
(3)
Statements: C % F, F @ G, G © M
Conclusions: I. M % F II. C @ G
A. if only conclusion I is true
B. if only conclusion II is true
C. if either conclusion I or II is true
D. if neither conclusion I nor II is true
E. if both conclusions I and II are true
Ans. D
As per the information given,
1. C % F means C > F
2. F @ G means F ≥ G
3. G © M means G ≤ M
So, the final equation will be,
C > F ≥ G ≤ M
Now, the Conclusion I. M % F means M > F
the Conclusion II. C @ G means C ≥ G
Let's check the Conclusions now,
Conclusion I:
Conclusion II:
Hence, neither Conclusion I nor II is true.
(4)
Statements: W $ K, K © G, G @ R
Conclusions: I. R $ K II. G % W
A. if only conclusion I is true
B. if only conclusion II is true
C. if either conclusion I or II is true
D. if neither conclusion I nor II is true
E. if both conclusions I and II are true
Ans. B
As per the information given,
1. W $ K means W < K
2. K © G means K ≤ G
3. G @ R means G ≥ R
So, the final equation will be,
W < K ≤ G ≥ R
Now, the Conclusion I. R $ K means R < K
the Conclusion II. G % W means G > W
Let's check the Conclusions now,
Conclusion I:
Conclusion II:
Hence, only Conclusion II is true.
For example,
@ denotes >
& denotes =
* denotes <
And so on.
Sometimes, to make the questions a bit more complicated, the reverse relations may be present in the question as:
A*B denotes B is not greater than A
Here, in this case, candidates will have to be more careful, while arranging the inequality operators between two elements.
Once, you have decoded the table, the next step is to combine the decoded statements in order to find out the relation between elements.
A > B = C < D
Now, you can look at the conclusions to find out which one of them is correct. This way, you will be able to minimise on any errors and ensure you score full marks in this topic.
Case of Missing inequalities
This category includes missing operator signs, which are required to be inserted between elements and then find out the relation between them.
At first, it may seem easy, but you need to carefully insert the signs to ensure you are able to arrive at the correct answer.
Example:
A ________ B > C = ≥ D
What sign will come in place of __________ to arrive at the answer A > D ?
A. >
B. <
C. =
D. ≤
So here, the correct sign will be (1) ie. >
This will ensure that all elements are in sync, to help you solve the question correctly.