Please wait...
/
-
Directions For Questions
Direction: In the following questions, the symbols #, @, $, % are used with the following meaning illustrated.
‘P # Q’ 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 not smaller than Q’‘P * Q’ means ‘P is not greater than Q’‘P & Q’ means ‘P is neither greater than nor smaller than Q’
...view full instructions
Statement:
A @ B, C $ B, D & C, D # E
Conclusion:
I. D # A
II. B # E
III. B @ E
Symbol
#
@
$
*
&
Meaning
>
<
≥
≤
=
Given statement: A @ B, C $ B, D & C, D # E
Decoded Form: A < B, C ≥ B, D = C, D > E
On combining: A < B ≤ C = D > E
Conclusions:
I. D # A → D > A → True (A < B ≤ C = D → A < D)
II. B # E → B > E → False (B ≤ C = D > E → relation cannot be determined)
III. B @ E → B < E → False (B ≤ C = D > E → relation cannot be determined)
IV D * B → D ≤ B → False (B ≤ C = D → B ≤ D)
Hence, only I is true
M $ N, N & O, P & O # Q, R @ Q
I. N @ R
II. O * M
III. R @ N
Given statement: M $ N, N & O, P & O # Q, R @ Q
Decoded Form: M ≥ N, N = O, P = O > Q, R < Q
On combining: M ≥ N = O = P > Q > R
I. N @ R → N < R → False (N = O = P > Q > R → N > R)
II. O * M → O ≤ M → True (M ≥ N = O → M ≥ O)
III. R @ N → R < N → True (N = O = P > Q > R→ N > R)
IV M # Q → M > Q → True (M ≥ N = O = P > Q → M > Q)
Hence, only II, III and IV are true.
U @ V $ W * X, W & Y $ Z
I. Z $ X
II. U # W
III.V $ Z
Given statement: U @ V $ W * X, W & Y $ Z
Decoded Form: U < V ≥ W ≤ X, W = Y ≥ Z
I. Z $ X → Z ≥ X → False (X ≥ W = Y ≥ Z → X ≥ Z)
II. U # W → U > W → False (U < V ≥ W → Relation can’t determine)
III.V $ Z → V ≥ Z → True (V ≥ W = Y ≥ Z → V ≥ Z)
IV U * Y → U ≤ Y = W→ False (U < V ≥ W = Y→ Relation can’t determine)
either applies in II and IV as all three relation are given.
Hence, Only III and either II or IV are true
A $ B # C * D, B # E, C * F
I. F # D
II. E @ A
III.E @ C
Given statement: A $ B # C * D, B # E, C * F
Decoded Form: A ≥ B > C ≤ D, B > E, C ≤ F
I. F # D → F > D → False (F ≥ C ≤ D → Relation can’t be determined)
II. E @ A → E < A → True (A ≥ B > E → A > E)
III. E @ C → E < C → False (E < B > C → Relation can’t be determined)
IV B # F → B > F → False (B > C ≤ F → Relation can’t be determined)
J * K @ L & M # N $ O
I. K # N
II. L @ J
III. N $ K
Given statement: J * K @ L & M # N $ O
Decoded Form: J ≤ K < L = M > N ≥ O
I. K # N → K > N → False (K < L = M > N → Relation can’t be determined)
II. L @ J → L < J → False (J ≤ K < L → J < L)
III. N $ K → N ≥ K → False (K < L = M > N → Relation can’t be determined)
IV M # O → M > O → True (M > N ≥ O → M > O)
All three combination is given between K and N that means either I or II is true
Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.
A + B means A is neither smaller than nor equal to B
A @ B means A is neither greater than nor equal to B
A * B means A is not smaller than B
A / B means A is not greater than B
A % B means A is neither greater than nor smaller than B
Statements:
P * Q; Q / R; R % S; S + T
I. P + Q
Let’s simplify these first:
A is
%
+
to B
Given statements: P * Q; Q / R; R % S; S + T
On Simplification: P ≥ Q; Q ≤ R; R = S; S > T
On Combining: . P ≥ Q ≤ R = S > T
I. P + Q → P > Q → False(as P ≥ Q; it is possible but not definite)
II. S + Q → S > Q → False (as S = R ≥ Q; it is possible but not definite)
P @ Q ; Q / R ; R * S ; S % T
I. P + S
Given statements: P @ Q; Q / R; R * S; S % T
On Simplification: P < Q; Q ≤ R; R ≥ S; S = T
On Combining: P < Q ≤ R ≥ S = T
I. P + S → P > S → False (P < Q ≤ R ≥ S = T, so definite relation between S and P cannot be determined)
II. R + P → R > P → True (as P < Q ≤ R)
P % Q; Q * R; R @ S; S + T
I. R * P
Given statements: P % Q; Q * R; R @ S; S + T
On simplification: P = Q; Q ≥ R; R < S; S > T
On combining: P = Q ≥ R < S > T
I. R * P → R ≥ P → False (as R ≤ P)
II. Q @ T → Q < T → False (P = Q ≥ R < S > T, so definite relation between Q and T cannot be determined)
A * B; B % C; C % D; D + E
I. A + E
Given statements: A * B; B % C; C % D; D + E
On Simplification: A ≥ B; B = C; C = D; D > E
On Combining: A ≥ B = C = D > E
I. A + E → A > E → True (A ≥ B = C = D > E)
II. B / D → B ≤ D → False (but B = D)
A @ B; B % C; C * D; D % E
Given statements: A @ B; B % C; C * D; D % E
On Simplification: A < B, B = C, C ≥ D, D = E
On Combining: A < B = C ≥ D = E
I. A + E → A > E → False (as A < B = C ≥ D = E, as clear relation between A and E cannot be determined)
II. B * D → B ≥ D → True (as B = C ≥ D)
Direction: In the following questions, the symbols @, $, *, © and # are used with the following meaning as illustrated below:
‘10 @ 30’ means ‘10 is greater than 30’.
‘10 $ 30’ means ‘10 is smaller than 30’
‘10 * 30’ means ‘10 is either greater than or equal to 30’
‘10 © 30’ means ‘10 is either smaller than or equal to 30’
‘10 # 30’ means ‘10 is not equal to 30’
Now in each of the following questions assuming the given statements to be true, find which of the conclusion/s given below them is/are definitely true?
20 @ 40, 50 # 40, 70 @ 50, 90 * 70, 90 © 80
I. 20 # 50
II. 50 $ 90
III. 50 * 70
According to the given information,
10 is
©
≠
to 30
On converting: 20 > 40, 50 ≠ 40, 70 > 50, 90 ≥ 70, 90 ≤ 80
On combining: 20 > 40 ≠ 50 < 70 ≤ 90 ≤ 80
I. 20 # 50 → 20 ≠ 50 → False (as 20 > 40 ≠ 50).
II. 50 $ 90 → 50 < 90 → True (as 50 < 70 ≤ 90).
III. 50 * 70 → 50 ≥ 70 → False (as 50 < 70).
Hence, only conclusion II is true.
100 © 90, 70 * 20, 90 @ 70, 40 # 80, 80 © 100
I. 80 © 90
II. 70 @ 40
III. 80 * 90
On converting: 100 ≤ 90, 70 ≥ 20, 90 > 70, 40 ≠ 80, 80 ≤ 100
On combining: 40 ≠ 80 ≤ 100 ≤ 90 > 70 ≥ 20
I. 80 © 90 → 80 ≤ 90 → True (as 80 ≤ 100 ≤ 90).
II. 70 @ 40 → 70 > 40 → False (as 40 ≠ 80 ≤ 100 ≤ 90 > 70 → clear relation between 70 and 40 can be determined).
III. 80 * 90 → 80 ≥ 90 → False (as 80 ≤ 100 ≤ 90).
Hence, only conclusion I is true.
50 # 100, 100 © 40, 60 @ 40, 50 © 70, 90 * 60
I. 70 # 100
II. 40 @ 60
III. 100 $ 90
50 # 100, 100 © 40, 60 @ 40, 50 © 70, 90 * 60,
On converting: 50 ≠ 100, 100 ≤ 40, 60 > 40, 50 ≤ 70, 90 ≥ 60
On combining: 70 ≥ 50 ≠ 100 ≤ 40 < 60 ≤ 90
I. 70 # 100 → 70 ≠ 100 → False (as 70 ≥ 50 ≠ 100 → there is no relation between 70 and 100 can be determined).
II. 40 @ 60 → 40 > 60 → False (as 40 < 60).
III.100 $ 90 → 100 < 90 → True (as 100 ≤ 40 < 60 ≤ 90).
Hence, only conclusion III is true.
40 * 60, 90 $ 80, 50 * 80, 60 © 90, 70 @ 40
I. 70 @ 60
II. 60 © 40
III. 50 @ 90
On converting: 40 ≥ 60, 90 < 80, 50 ≥ 80, 60 ≤ 90, 70 > 40
On combining: 70 > 40 ≥ 60 ≤ 90 < 80 ≤ 50
I. 70 @ 60 → 70 > 60 → True (as 70 > 40 ≥ 60).
II. 60 © 40 → 60 ≤ 40 → True (as 40 ≥ 60 ≤ 90).
III. 50 @ 90 → 50 > 90 → True (as 90 < 80 ≤ 50).
Hence, all the conclusions are true.
70 @ 80, 70 # 90, 60 * 80, 60 * 50, 40 $ 50
I. 80 @ 60
II. 80 * 50
III. 70 $ 60
On converting: 70 > 80, 70 ≠ 90, 60 ≥ 80, 60 ≥ 50, 40 < 50
On combining: 90 ≠ 70 > 80 ≤ 60 ≥ 50 > 40
I. 80 @ 60 → 80 > 60 → False (as 80 ≤ 60).
II. 80 * 50 → 80 ≥ 50 → False (as 80 ≤ 60 ≥ 50 → clear relation can be determined between 80 and 50).
III. 70 $ 60 → 70 < 60 → False (as 70 > 80 ≤ 60 → clear relation can be determined between 70 and 60).
Hence none of the conclusion is true.
Correct (-)
Wrong (-)
Skipped (-)
Time Taken: - 
×
Bank
SSC
Railway
State
Other
Teaching
Insurance
Medical
Engineering
Defence
GATE
NTA CUET
UPSC
MBA Entrance
LAW
WBJEE 2025
JEE Advanced 2025
CUET UG 2025
RRB NTPC 2024-25
Railway Group D 2025
Bihar Police Constable 2025
RRB ALP CBT-I 2025
Get latest Exam Updates 
