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Coded Inequalities Test

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Reasoning based on Coded Inequalities

  • This online quiz will test your knowledge of Coded Inequalities in Reasoning Ability.
  • This Online Test is useful for academic and competitive exams.
  • Multiple answer choices are given for each question in this test. You have to choose the best option.
  • After completing the test, you can see your result.
  • There is no negative marking for wrong answers.
  • There is no specified time to complete this test.

Directions (Q.1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’.
Statements: B $ K, K @ D, D # M
Conclusions:I. B $ M II. B @ M

B = K ...(i)
K < D ...(ii) D > M ...(iii)
From (i) and (ii), we get D > K = B ...(iv)
From (iii) and (iv), no specific relation can be obtained between B and M. Therefore, B = M (Conclusion I) and B < M (Conclusion II) are not necessarily true.

Directions (Q.1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’.
Statements: H @ N, N © W, W # V
Conclusions: I. H @ V II. V @ N

H < N ... (i) N > W ...(ii)
W ≥ V ...(iii)
From (ii) and (iii), we get N > W ≥ V ...(iv)
From (i) and (iv), no specific relation can be obtained between H and V. Hence, H < V (Conclusion I) is not necessarily true. But V < N (Conclusion II) follows from equation (iv).

Directions (Q.1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’.
Statements:J * D, Q # D, Q @ M
Conclusions:I. Q © J II. Q $ J

J ≤ D ...(i)
Q ≥ D ...(ii)
Q < M ...(iii) Combining (i) and (ii), we get Q ≥ D ≥ J ⇒ Q > J (Conclusion I) or Q = J (Conclusion II). Hence, either conclusion I or conclusion II is true.

Directions (Q.1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’.
Statements:F # G, N $ G, N © T
Conclusions:I. T © F II. N * F

F ≥ G ...(i)
N = G ... (ii)
N > T ... (iii)
Combining all, we get F ≥ G = N > T ⇒ N ≤ F (Conclusion II) and T < F. Hence, conclusion I (T > F) is not true but conclusion II is true.

Directions (Q.1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’.
Statements:M © R, R @ K , K $ T
Conclusions:I. T © R II. T © M

M > R ...(i)
R < K ...(ii) K = T ... (iii) Combining (ii) and (iii), we get K= T > R
⇒ T > R (Conclusion I).
On the basis of the given information no specific relation can be obtained between T and M. Hence, T > M (Conclusion II) is not necessarily true.

Directions (Q.6-10): ‘P Q’ means P is not equal to Q. ‘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 to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.
Statements : K © M, M R, R ? T
Conclusions : I. K © T II. M ? T

K ≥ M ... (i)
M ≠ R ...(ii); R = T ...(iii)
Combining all equations, we get K ≥ M ≠ R = T ⇒ M ≠ T
From this we can’t get any specific relation between K and T. Hence, conclusion I is not true. Conclusion II is false since M ≠ T.

Directions (Q.6-10): ‘P Q’ means P is not equal to Q. ‘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 to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.
Statements : B + D, D @ N, N $ H
Conclusions : I. M © D II. H © N

B < D ...(i)
D > N ...(ii)
N ≤ H ...(iii)
From equations (ii) and (iii), we can’t obtain any specific relation between H and D. Hence, conclusion I (H ≥ D) is not true. But conclusion II (H ≥ N) follows from equation (iii)

Directions (Q.6-10): ‘P Q’ means P is not equal to Q. ‘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 to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.
Statements : M © K, K@ P, P $ N
Conclusions : I. M @ NII. M ? N

M ≥ K ... (i)
K > P ...(ii)
P ≤ N ...(iii)
Combining (i) and (ii), we get M ≥ K > P ...(iv)
From (iii) and (iv), no specific relation can be obtained between M and N. Hence, conclusion I (M > N) and conclusion II (M = N) are not true.

Directions (Q.6-10): ‘P Q’ means P is not equal to Q. ‘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 to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.
Statements : T $ M, M ? Q, Q + R
Conclusions : I. Q @ TII. Q ? T

T ≤ M ...(i)
M = Q ...(ii)
Q < R ...(iii)
Combining (i) and (ii) we getM = Q ≥ T ⇒ Q > T (Conclusion I) or Q = T (Conclusion II)

Directions (Q.6-10): ‘P Q’ means P is not equal to Q. ‘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 to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.
Statements : D @ B, B $ T, T + M
Conclusions : I. M @ BII. T © B

D > B ... (i)
B ≤ T ...(ii)
T < M ...(iii)
Combining (ii) and (iii), we get M > T ≥ B ⇒ M > B (Conclusion I) and T ≥ B (Conclusion II).

Directions (Q.11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater than Q. ‘P × Q’ means P is neither smaller than nor equal to Q. ‘P # Q’ means P is neither greater than nor equal to Q.
Statements : Z $ K, K × T, T © F
Conclusions : I. F # ZII. Z × T

Directions (Q.11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater than Q. ‘P × Q’ means P is neither smaller than nor equal to Q. ‘P # Q’ means P is neither greater than nor equal to Q.
Statements : K × B, B @ D, D # K
Conclusions : I. B @ KII. B # K

K > B …(i)
B ≤ D …(ii)
D < K …(iii)
From (i), B < K. Hence II is true but I is not true.

Directions (Q.11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater than Q. ‘P × Q’ means P is neither smaller than nor equal to Q. ‘P # Q’ means P is neither greater than nor equal to Q.
Statements : N © R, R @ M, M $ J
Conclusions : I. N © MII. N # M

N = R ...(i),
R ≤ M ...(ii)
M ≥ J ...(iii)
From (i) and (ii), we get N = R ≤ M ⇒ N ≤ M. Hence either I or II is true.

Directions (Q.11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater than Q. ‘P × Q’ means P is neither smaller than nor equal to Q. ‘P # Q’ means P is neither greater than nor equal to Q.
Statements : S $ T, T @ R, R # M
Conclusions : I. M × TII. M© T

S ≥ T ...(i),
T ≤ R ... (ii)
R < M ... (iii)
From (ii) and (iii), we get T ≤ R < M ⇒ T < M or M > T. Hence I is true and II is not true.

Directions (Q.11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater than Q. ‘P × Q’ means P is neither smaller than nor equal to Q. ‘P # Q’ means P is neither greater than nor equal to Q.
Statements : H @ V, V © M, M × R
Conclusions : I. R × HII. H × R

H ≤ V ... (i)
V = M ... (ii)
M > R ... (iii)
Combining all, we get H ≤ V = M > R ⇒ no relationship between H and R can be established. Since conclusions I and II are not exhaustive, neither of them is true.

Directions (Q.16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.
Statements : S * K, T & K, K * B
Conclusions : I. S $ BII. S @ B

S ≥ K... (i); T < K ... (ii)
K ≥ B ... (iii)
Combining (i) and (iii), we get S ≥ K ≥ B. Hence, S > B or S = B. Therefore either conclusion I or II is true.

Directions (Q.16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.
Statements : Y $ Z, H $ D, Z * D
Conclusions : I. D £ YII. H £ Z

Combining all the three statements, we get Y = Z ≥ D = H. Therefore D ≤ Y and H ≤ Z are true.

Directions (Q.16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.
Statements : M @ N, P @ R, P & N
Conclusions : I. P £ MII. R & N

Combining all the three statements together we get M > N > P > R. Therefore P ≤ M is not true, but R < N is true.

Directions (Q.16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.
Statements : T & K, K * B, S * K
Conclusions : I. B * TII. S £ T

Combining I and III, we get S ≥ K > T. Therefore S ≤ T is not true. We have no information about the relationship between B and T.

Directions (Q.16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.
Statements : P @ R, M @ N, P & N
Conclusions : I. N @ RII. P & M

Combining all the three statements, we get M > N > P > R. Therefore N > R and P < M are true.

Directions (Q.21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
Statements : M $ K,D * K,R # K
Conclusions : I. D $ MII. M % D

M = K .…. (i)
D ≤ K ….. (ii)
R < K ..… (iii)
From (i) and (ii), we get M = K ≥ D ⇒ M ≥ D
Hence, either M > D (conclusion II) or M = D (conclusion I) is true

Directions (Q.21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
Statements : F * M, M % R, E @ F
Conclusions : I. M % EII. R @ E

F ≤ M … (i)
M > R … (ii)
E ≥ F … (iii)
From (i) and (iii), no specific relation can be obtained between M and E. Similarly, no specific relation can be obtained between R and E.

Directions (Q.21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
Statements : H $ K, T # H, W * T
Conclusions : I. K % WII. T # K

H = K … (i)
T < H …(ii)
W ≤ T …(iii)
From (i), (ii) and (iii), we get K = H > T ≥ W ⇒ K > W (conclusion I) and T < K (conclusion II).

Directions (Q.21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
Statements : N % A, A # L, F $ N
Conclusions : I. L % FII. F % A

N > A … (i)
A < L … (ii)
F = N …(iii)
From (i) and (iii), we get F = N > A ⇒ F > A (conclusion II). But no specific relation can be obtained between L and F. Hence, conclusion I is not necessarily true.

Directions (Q.21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
Statements : B * D,D $ M, F % M
Conclusions : I. B # MII. F % B

B ≤ D …(i)
D = M …(ii)
F > M …(iii)
From (i), (ii) and (iii), we get F > M = D ≥ B ⇒ B ≤ M and F > B (conclusion II). Since, B ≤ M, therefore, conclusion I is not necessarily true.

Directions (26-30): Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?
Statement : W ≥ D < M < P < A = F
Conclusion : I. F > DII. P < W

W ≥ D < M < P < A = F
or F > D
So I follows.
No relation can be established between P and W. So II does not follow.

Directions (26-30): Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?
Statement : H ≥ M > F < A = B > S
Conclusion : I. H > BII. F < S

H ≥ M > F < A = B > S
No relation can be established between (H, B) and (F, S).
So none follows.

Directions (26-30): Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?
Statement : B > T > Q > R = F
Conclusions : I. Q ≥ FII. T > F

B > T > Q > R = F
or Q > F and T > F
So, only II follows.

Directions (26-30): Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?
Statement : S = R ≥ Q, P < Q
Conclusion : I. S ≥ PII. R > P

S = R ≥ Q > P
or S > P and R > P
So, only II follows.

Directions (26-30): Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?
Statement : S ≥ M < Y = Z > F > T
Conclusion : I. S > FII. Y > T

S ≥ M < Y = Z > F > T
or Y > T
So, only II follows.

Directions (Q.31-35): ‘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 smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.
Statements : J © T, T * B, B @ R
Conclusions : I. J @ RII. R % T III. J @ B

J > T ...(i)
T ≤ B ....(ii)
B < R ... (iii)
From (ii) and (iii), we get R > B ≥ T ... (iv)
Hence, no specific relation can be obtained between (i) J and R or (ii) J and B. Hence, neither I nor III follows. From equation (iv) we get R > T. Therefore, conclusion II does not follow.

Directions (Q.31-35): ‘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 smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.
In each of the following questions assuming the given statements to be true, find which of the conclusions given below are definitely true.
Statements : T * M, K @ M, K × Z
Conclusions : I. T @ Z II. Z @ M III. M % Z

T ≤ M ... (i)
K< M ...(ii)
K ≥ Z ... (iii)
From (ii) and (iii), we get M > K ≥ Z ...(iv).
⇒ M > Z Hence, conclusion II (Z < M) follows.
But conclusion III (M = Z) does not follow. Again, no specific relation can be obtained between T and Z. Hence, conclusion I does not follow.

Directions (Q.31-35): ‘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 smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.
Statements : K * N, N% T, R @ T
Conclusions : I. K @ R II. T © K III. R % K

K ≤ N ...(i)
N = T ...(ii)
R < T ...(iii)
From (i) and (ii), we get T = N ≥ K ...(iv)
From (ii) and (iii), we get T = N > R ...(v)
From equation (iv), we get T ≥ K. Hence, conclusion II (T > K) is not necessarily true.
From equations (iv) and (v) we can’t obtain any specific relation between K and R. There fore, conclusion I and conclusion III do not follow. Thus, no conclusion follows.

Directions (Q.31-35): ‘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 smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.
Statements : H © M, M × D, T @ D
Conclusions : I. T @ MII. H © D III. H % D

H > M ... (i)
M ≥ D ... (ii)
T < D ... (iii)
From (i), (ii) and (iii), we get H > M ≥ D > T...(iv)
From equation (iv), we get H > T. This implies T < M.
Hence, conclusion I follows. Again, H > D. Hence II follows but III does not.

Directions (Q.31-35): ‘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 smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.
Statements : W × M, M © F, D * F
Conclusions : I. D@WII. M©D III. F@W

W ≥ M ... (i)
M > F ... (ii)
D ≤ F ...(iii)
From (i), (ii) and (iii), we get W ≥ M > F ≥ D...(iv)
From (iv); we get W > D. Hence, conclusion I (D < W) follows. Again, from the equation (iv), we get M > D. Hence, conclusion II (M > D) follows. Again, from the equation (iv), we get W > F. Hence, conclusion III (F < W) follows.

Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that ‘V > Z’ definitely holds true ?
V__ W__ X__ Z

V > W ≥ X > Z
or V > Z

Which of the following symbols should replace the question mark in the given expression in order to make the expressions ‘M ≤ K’ as well as ‘L > P’ definitely true ?
K ≥ L ? M > N > P

K ≥ L = M > N > P
or M ≤ K and L > P

In which of the following expressions will the expressions ‘H < F’ as well as ‘J > H’ be definitely true?

F ≥ G = H ≤ I < J
or H ≤ F and J > H

Which of the following expressions will be true if the given expression ‘A < C ≥ B = D ≤ E’ is definitely true?

A < C ≥ B = D ≤ E
None of the four is true.

In which of the following expressions will the expression ‘L > P’ be definitely false?

P = N ≥ L > M
or L ≤ P

Now check your Result..

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