Inequality Questions PDF Download
Symbols and
Meanings in Inequalities
Symbol |
What does it mean? |
Example |
> |
Greater than |
A > B → A is greater than
B |
< |
Less than |
A < B → A is less than B |
≥ |
Greater than or equal to |
A ≥ B → A is greater than or
equal to B |
≤ |
Less than or equal to |
A ≤ B → A is greater than or
equal to B |
= |
Equal to |
A = B → A is equal to B |
1. A relationship can be easily
established between two elements if they have similar signs.
For
e.g.
A > B > C > D
Here
we can draw a conclusion – A > D, B > D, A > C or D < A, D < B
or C < A, C < B
2. A relationship cannot be
easily established between two elements if they don’t have similar signs. In
these cases, you have to put extra care seeking either-or cases type
conclusions.
For
e.g.
A > B < C > D
Here
relationship cannot be established between – A & C, A & D, B &
D.
Few of the questions related to Inequality are given below:-
Directions (1-5): In the following questions, the
symbols >, <, %, = and ≥ are used with the following meaning as
illustrated below-
‘P>Q’
means ‘P is neither greater than nor equal to Q’
‘P<Q’
means ‘P is neither equal to nor smaller than Q’
‘P%Q’
means ‘P is neither smaller than nor greater than Q’
‘P=Q’
means ‘P is not smaller than Q’
‘P≥Q’
means ‘P is not greater than Q’
Now in
each of the following questions assuming the given statement to be true, find
which of the conclusions given below them is/are definitely true and give
your answer accordingly.
Q1.
Statements: P > X = B < I ≥ O
Conclusions:
I. P>B II. B=O
(a) None
is true
(b) Only
I is true
(c) Only
II is true
(d)
Either I or II is true
(e) Both
are true
Q2.
Statements: A = B, B % M, K < M
Conclusions:
I. A<M
II. B % A
(a) Only
I true
(b) Only
II true
(c) Only
I and II are true
(d)
Either I or II is true
(e) None
of these
Q3.
Statements: R = M, M ≥ Z, Z % A, Y > Z
Conclusions:
I. Y >
A II. M ≥ A
(a) None
is true
(b) Only
I is true
(c) Both
I and II are true
(d) Only
II is true
(e) None
of these
Q4.
Statements: A = B, B % M, K < M
Conclusions:
I. K
< B II. A % M
(a) None
follows
(b) Only
I is true
(c) Only
II is true
(d)
Either I or II is true
(e) None
of these
Q5.
Statements P > X = B < I ≥ O>K
Conclusions:
I. I >
K II. X = I
(a) None
follows
(b) Only
I is true
(c) Only
I and II are true
(d) Only
II is true
(e) None
of these
Solutions
(1-5):
S1.
Ans.(a)
I. P>B
(false) II. B=O (false)
S2.
Ans.(d)
I. A<M(false)
II. B % A(false)
S3.
Ans.(c)
I. Y
> A(true) II. M ≥ A(true)
S4.
Ans.(b)
I. K
< B(true) II. A % M(false)
S5.
Ans.(b)
I. I >
K(true) II. X = I(False)
Directions
(6-10): In the following questions, the symbols @, #, %, $ and © are used with
the following meaning as illustrated below-
‘P#Q’
means ‘P is neither greater than nor equal to Q’
‘P©Q’
means ‘P is neither equal to nor smaller than Q’
‘P%Q’
means ‘P is neither smaller than nor greater than Q’
‘P$Q’ means
‘P is not smaller than Q’
‘[email protected]’ means
‘P is not greater than Q’
Now in
each of the following questions assuming the given statement to be true, find
which of the three conclusions I, II and III given below them is/are definitely
true and give your answer accordingly.
Q6.
Statements: M © S @ Z % R $ N
Conclusions:
I. M ©
Z II. R $ M III.S © N
(a) None
is true
(b) Only
I is true
(c) Only
III is true
(d)
Either I or II is true
(e) All
are true
Q7.
Statements: A $ B, B % M, K © M
Conclusions:
I. K ©
B II. M @ A III. A © K
(a) Only
I and III are true
(b) Only
II and III are true
(c) Only
I and II are true
(d) All
are true
(e) None
of these
Q8.
Statements: R $ M, M © Z, Z @ A, Y © Z
Conclusions:
I. R © Y
II. Z # R III.Y © R
(a) None
is true
(b) Only
II is true
(c) Only
I and II are true
(d) Only
II and III are true
(e) All
are true
Q9.
Statements: M © S @ Z % R $ N
Conclusions:
I. N #
Z II. R # M III. S % N
(a) None
follows
(b) Only
I is true
(c) Only
III is true
(d)
Either I or II is true
(e) All
are true
Q10.
Statements: R $ M, M © Z, Z @ A, Y © Z
Conclusions:
I. R ©
Z II. Z # A III.R % A
(a) Only
I is true
(b) Only
II is true
(c) Only
I and II are true
(d) Only
II and III are true
(e) All
are true
Solutions
(6-10):
S6.
Ans.(d)
I. M © Z
(false) II. R $ M(false) III.S © N(false)
S7.
Ans.(c)
I. K ©
B(true) II. M @ A(true) III. A © K(false)
S8.
Ans.(b)
I. R ©
Y(false) II. Z # R(true) III.Y © R(false)
S9.
Ans.(a)
I. N #
Z(false) II. R # M(false) III. S % N(false)
S10.
Ans.(a)
I. R ©
Z(true) II. Z # A(false) III.R % A(false)
Directions
(11-15): In the following questions, the symbols @, ^, *, # and ! used with the
following meaning as illustrated below:
‘P ^ Q’ means
‘P is not smaller than Q’
‘[email protected]’ means
‘P is neither smaller than nor equal to Q’
‘P # Q’ means
‘P is neither greater than nor equal to Q’
‘P % Q means
“P is neither greater than nor smaller than Q’
‘P !Q’ means
‘P is not greater than Q’
Now, in
each of the following questions assuming the given statements to be true, find
which of the four conclusions I, II, III and IV is/are definitely true and give
your answer accordingly.
Q11.
Statements: A ! B ^ C @ D # M
Conclusions:
I. B @ D II. [email protected] M
III. A ! M IV. C # B
(a) Only
I is true
(b) Only
III is true
(c) Only
IV is true
(d) Only
either III or IV is true
(e) Only
either III or II and I are true
Q12.
Statements: A ! Z, Z ^ J, J # X, X @ L
Conclusions:
I. L # J II. Z @ X
III. A # X IV. [email protected] L
(a) None
is true
(b) Only
I is true
(c) Only
II is true
(d) Only
III is true
(e) Only
IV is true
Q13.
Statements: A ! B ^ C @ D # M
Conclusions:
I. C ! B II. D # C
III. C @ M IV. B @ A
(a) Only
I and II are true
(b) Only
I, II and IV are true
(c) Only
II, III and IV are true
(d) Only
I, III and IV are true
(e) All
I, II, III and IV are true
Q14.
Statements: A ! Z, Z ^ J, J # X, X @ L
Conclusions:
I. A @ X II. X
^ A
III. J ! L IV. Z % X
(a) None
is true
(b)
Either I or II is true
(c) Only
II is true
(d) Only
III is true
(e) Only
IV is true
Q15.
Statements: H ^ G, G @ I, I ! J, J # K
Conclusions:
I. I # K
II. H ^ J
III. G @ K IV. H
@ I
(a) Only
I and II are true
(b) Only
I is true
(c) Only
III and IV are true
(d) Only
III is true
(e) Only
I and IV is true
Solutions
(11-15):
S11. Ans.(e)
Sol. : I. B @ D(true)
II. [email protected] M (false)
III. A !
M(false) IV. C # B(false)
S12. Ans.(a)
Sol. : I. L #
J(false) II. Z @ X(false)
III. A #
X(false) IV. [email protected] L(false)
S13. Ans.(a)
Sol. : I. C ! B(true) II. D # C(true)
III. C @
M(false) IV. B @ A(false)
S14. Ans.(b)
Sol. : I. A @ X(false) II.
X ^ A(false)
III. J ! L(false)
IV. Z % X(false)
S15. Ans.(e)
Sol. I. I #
K(true) II. H ^
J(false)
III. G @
K(false) IV. H @ I(true)