Inequality Questions for competitive exams
Before solving Inequality questions be thorough with basic inequality relations.Make sure that you are thorough with inequality statements and conclusion that follows
No need to ‘memorize’ this table as whole. Just read and understand .Now let us practice some simple problems.
No need to ‘memorize’ this table as whole. Just read and understand .Now let us practice some simple problems.
Solving Inequality questions
Example1:Satements:A>B,B=C≥D
Conclusions:1.A=C
2.A>C
3.D>A
Options.1 .1 and 2 are true
2. 2 and 3 are true
3. Only 2 is true
4. Either 1 or 2 is true
‘P&Q’ means ‘P’ is greater than ‘Q’.
‘P%Q’ means ‘P’ is smaller than ‘Q’.
‘P@Q’ means ‘P’ is either greater than or equal ‘Q’.
‘P$Q’ means ‘P’ is either smaller than or equal to ‘Q’.
‘P#Q’ means ‘P’ is equal to ‘Q’.
Assuming the Statements given in each of the question as true deduce which of the two inferences 1 and 2 is/are true.
A) If only conclusion I is true.
B) If only conclusion II is true.
C) If either conclusion I or II is true.
D) If neither conclusion I nor II is true.
E) If both conclusions I and II are true1)
Q1.statement N%P,P&R,R$L
Inference:1. N$L 2. N@L
Solution: lets rewrite the statement and inference
Q1.statement N<P,P>R,R≤L
Inference:1 .N≤L
2. N>L
Relation between N and L
N<P>R<L or N<P>R=L
N<P>R<L or N<P>L
Either N<L,N>L or N=L ,which can be also written as N≤L or N>L.( Note:N≤L and N>L will form complementary pair)
Thus answer is C.
(Tip: successive similar signs ‘> > > > > …>’ will be replaced by a single ‘>’ and ‘<<<<<<<<…..<’ will be replaced by a single ‘<’. No replacement is possible if signs are mixed like ‘< >’ or ‘> <’ )
Conclusions:1.A=C
2.A>C
3.D>A
Options.1 .1 and 2 are true
2. 2 and 3 are true
3. Only 2 is true
4. Either 1 or 2 is true
Solution:
Relation between A and C
Relation between A and C
A>B=C
A>C
A>C
Relation between A and D
A>B,B=C≥D
A>B=C≥D
A>C≥D
A>D
D<A
So answer is option 2
Example2.Statements P<Q≥R,R≤S=T,T<U
Conclusions:1.P≥T
2.R≤U
A>B,B=C≥D
A>B=C≥D
A>C≥D
A>D
D<A
So answer is option 2
Example2.Statements P<Q≥R,R≤S=T,T<U
Conclusions:1.P≥T
2.R≤U
3.P<S
Options:1. 1 and 2 are true
2. 2 and 3 are true
3.only 3 is true
4.None is true
Solution:
Relation between P and T
P<Q≥R,R≤S=T
P<Q≥R≤S=T
P<Q≥R≤T
P<Q>R≤T or P<Q=R≤T
P<Q>R<T or P<Q>R=T or P<Q=R=T or P<Q=R<T
P<Q>R<T or P<Q>T or P<T
Either P=T or P<T or P>T(no definite conclusion)
Relation between R and U
R≤S=T,T<U
R≤S=T<U
R≤S<U
R<U
Options:1. 1 and 2 are true
2. 2 and 3 are true
3.only 3 is true
4.None is true
Solution:
Relation between P and T
P<Q≥R,R≤S=T
P<Q≥R≤S=T
P<Q≥R≤T
P<Q>R≤T or P<Q=R≤T
P<Q>R<T or P<Q>R=T or P<Q=R=T or P<Q=R<T
P<Q>R<T or P<Q>T or P<T
Either P=T or P<T or P>T(no definite conclusion)
Relation between R and U
R≤S=T,T<U
R≤S=T<U
R≤S<U
R<U
Relation between P and S
S=T
So relation between P and S is same as P and T
So answer is option4.
S=T
So relation between P and S is same as P and T
So answer is option4.
Coded inequality
In coded inequality , inequality symbols (<,>,=,≥ and ≤) are replaced by some other symbols.
Example:In the following questions, the symbols $,@,%, & and # are used with the following meanings as illustrated below:‘P&Q’ means ‘P’ is greater than ‘Q’.
‘P%Q’ means ‘P’ is smaller than ‘Q’.
‘P@Q’ means ‘P’ is either greater than or equal ‘Q’.
‘P$Q’ means ‘P’ is either smaller than or equal to ‘Q’.
‘P#Q’ means ‘P’ is equal to ‘Q’.
Assuming the Statements given in each of the question as true deduce which of the two inferences 1 and 2 is/are true.
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 true1)
Q1.statement N%P,P&R,R$L
Inference:1. N$L 2. N@L
Solution: lets rewrite the statement and inference
Q1.statement N<P,P>R,R≤L
Inference:1 .N≤L
2. N>L
Relation between N and L
N<P>R<L or N<P>R=L
N<P>R<L or N<P>L
Either N<L,N>L or N=L ,which can be also written as N≤L or N>L.( Note:N≤L and N>L will form complementary pair)
Thus answer is C.
(Tip: successive similar signs ‘> > > > > …>’ will be replaced by a single ‘>’ and ‘<<<<<<<<…..<’ will be replaced by a single ‘<’. No replacement is possible if signs are mixed like ‘< >’ or ‘> <’ )