Question 1

Given: M > N > O, O ≥ P, P > Q, Q ≤ R

Which of the following is INDETERMINATE (cannot be determined)?

Accepted Answer

From the chain: M > N > O ≥ P > Q ≤ R. We can determine: M > O (true), N > P (true), M > Q (true), O > Q (true). However, the relationship between Q and R is Q ≤ R, which means R ≥ Q, but we don't know if R > Q or R = Q. More importantly, we cannot determine the relationship between M and R because M is in the upper chain and R is only constrained to be ≥ Q, with no connection between the upper chain and R.

Question 2

Given: A > B, B ≥ C, C > D, D = E, E < F

Which of the following conclusions is definitely TRUE?

Accepted Answer

From the given inequalities: A > B ≥ C > D = E < F. We can chain comparisons: A > B, B ≥ C, C > D, and D = E. Therefore A > C is true (transitive property through B). A > D is true (A > B > D). A > E is true (since D = E and A > D). However, we cannot determine the relationship between A and F because F > E but we don't know how F compares to A.

Question 3

Given: P ≤ Q, Q < R, R ≥ S, S > T, T ≥ U

Which conclusion is DEFINITELY FALSE?

Accepted Answer

From the chain: P ≤ Q < R ≥ S > T ≥ U. We know: P ≤ Q (true), Q < R (true), R ≥ S (true), S > T (true), T ≥ U (true). We can derive: P < R (P ≤ Q < R), S > U (S > T ≥ U), Q < S is indeterminate (Q < R but R ≥ S doesn't tell us if Q < S). The statement 'U > S' contradicts S > T ≥ U, so U > S is definitely false.

Question 4

Given: X ≥ Y, Y > Z, Z ≤ W, W < V, V = U. Which of the following is INDETERMINATE?

Accepted Answer

From the chain: X ≥ Y > Z ≤ W < V = U. We know X ≥ Y (could be equal), Y > Z (strict), Z ≤ W (could be equal), W < V (strict), V = U (equal). Definite conclusions: X > Z, Y > Z, W < V, V = U. Indeterminate: X vs. W (X could be greater, less, or equal to W), X vs. V (indeterminate), Y vs. W (indeterminate).

Question 5

Given: A < B, B ≤ C, C = D, D > E, E ≥ F

Which of the following conclusions is DEFINITELY FALSE?

Accepted Answer

From the chain: A < B ≤ C = D > E ≥ F. We can derive: A < C (true), A < D (true), B ≤ D (true), C > E (true), D > F (true), A < B (true), E ≥ F (true). The statement 'B > D' is false because B ≤ C and C = D means B ≤ D, so B > D contradicts this. The statement 'F > E' is false because E ≥ F means F ≤ E, so F > E is definitely false.

Question 6

Given: X ≥ Y, Y > Z, Z ≤ W, W < V, V ≥ X

Which conclusion is definitely TRUE?

Accepted Answer

From the given: X ≥ Y > Z ≤ W < V ≥ X. This creates a circular relationship. We know: X ≥ Y (true), Y > Z (true), Z ≤ W (true), W < V (true), V ≥ X (true). From V ≥ X and X ≥ Y, we get V ≥ Y. From Y > Z and Z ≤ W < V, we get Y > Z. The key insight: V ≥ X ≥ Y > Z, so V > Z is definitely true. Also, from the chain, we can confirm Y > Z is true.

Question 7

Given: M < N, N ≤ O, O > P, P ≥ Q, Q = R. Which conclusion is DEFINITELY TRUE?

Accepted Answer

From the chain: M < N ≤ O > P ≥ Q = R. We can deduce: M < N (given), M < O (transitive through N), N ≤ O (given), O > P (given), P ≥ Q (given), Q = R (given). However, we cannot determine M vs. P, M vs. Q, M vs. R, N vs. P, N vs. Q, N vs. R, or O vs. Q, O vs. R definitively.

Question 8

Given: M > N ≥ O, P < O, Q ≤ N, and R > M. Which of the following conclusions is DEFINITELY TRUE? (A) R > O (B) Q < O (C) P < N (D) R ≥ N

Accepted Answer

From the given inequalities: M > N ≥ O, P < O, Q ≤ N, R > M. Step 1: Chain M > N ≥ O, so M > O. Step 2: P < O, so P is less than O. Step 3: Q ≤ N, so Q is at most N. Step 4: R > M, so R is greater than M. Test each option: (A) R > O? R > M > N ≥ O, so R > O is DEFINITELY TRUE. (B) Q < O? Q ≤ N and N ≥ O. If N = O and Q = N, then Q = O, not Q < O. So this is not definitely true. (C) P < N? P < O and O ≤ N. If O = N, then P < N. But if O < N, then P < O < N, so P < N. Actually, P < O ≤ N means P < N is DEFINITELY TRUE. (D) R ≥ N? R > M > N, so R > N, which means R ≥ N is true. But (A) is more direct. Both (A) and (C) are definitely true. Let me verify: (A) R > M > N ≥ O, so R > O. TRUE. (C) P < O ≤ N, so P < N. TRUE. For a single correct answer, (A) is the most direct: R > M and M > O gives R > O via transitivity.

Question 9

Given: M < N ≤ O, P > O, Q ≥ M, and R = N.
Which of the following conclusions is INDETERMINATE (cannot be confirmed as definitely true or false)?

Accepted Answer

From the inequalities: M < N ≤ O < P and Q ≥ M and R = N. The relationship between Q and O cannot be determined because Q ≥ M and M < N ≤ O, so Q could be anywhere from M upwards, including above, equal to, or below O.

Question 10

Given: J ≥ K > L, M ≤ L, N < K, and O = J.
Which of the following conclusions is definitely FALSE?

Accepted Answer

From the inequalities: J ≥ K > L ≥ M (since M ≤ L) and N < K and O = J. The statement 'N ≥ L' is definitely FALSE because N < K and K > L does not guarantee N ≥ L. In fact, N could be anywhere below K, including below L.

Question 11

Given: A > B ≥ C, D < C, E ≤ B, and F > E. Which of the following conclusions is DEFINITELY TRUE? (A) F > D (B) A > E (C) D < B (D) F ≥ C

Accepted Answer

From the given inequalities: A > B ≥ C, D < C, E ≤ B, F > E. Step 1: Establish the chain: A > B ≥ C > D (since D < C). Step 2: E ≤ B, so E could equal B or be less than B. Step 3: F > E, but we don't know F's relationship to C or D. Test each option: (A) F > D? No. F > E, but E could be much smaller than D. For example: E = 1, F = 2, D = 3. F is not necessarily > D. (B) A > E? Yes. Since A > B and E ≤ B, we have A > B ≥ E, so A > E is ALWAYS true. (C) D < B? Yes, this is also true (D < C ≤ B). But let's verify (B) first. (D) F ≥ C? No. F > E, but E could be 0 and C could be 100. No guaranteed relationship. Both (B) and (C) appear true. However, (C) is derivable but (B) is the most direct from the chain. Re-checking: A > B ≥ C, E ≤ B. Therefore A > E is DEFINITELY TRUE. Actually, (C) D < B is also definitely true: D < C ≤ B implies D < B. The question asks for ONE correct answer. (B) A > E is the strongest conclusion because it directly chains A > B ≥ E.

Question 12

Given: X ≤ Y < Z, A > Z, B ≥ Y, and C < X. Which of the following conclusions is DEFINITELY FALSE? (A) A > Y (B) B > C (C) C ≥ X (D) A ≤ B

Accepted Answer

From the given inequalities: X ≤ Y < Z, A > Z, B ≥ Y, C < X. Step 1: Chain X ≤ Y < Z, so X < Z. Step 2: A > Z, so A is greater than Z. Step 3: B ≥ Y, so B is at least Y. Step 4: C < X, so C is less than X. Test each option: (A) A > Y? A > Z > Y, so A > Y is DEFINITELY TRUE. (B) B > C? B ≥ Y > X > C, so B > C is DEFINITELY TRUE. (C) C ≥ X? Given C < X, this is DEFINITELY FALSE. (D) A ≤ B? A > Z and B ≥ Y. Since Z > Y, we have A > Z > Y ≤ B. But A could be much larger than B. For example, A = 100, Z = 50, Y = 40, B = 40. Then A > B, so A ≤ B is not necessarily true, but it's not definitely false either—it's indeterminate. The answer is (C) because C < X directly contradicts C ≥ X.

Question 13

Given: P ≥ Q > R, S ≤ R, T < Q, and U = P.
Which of the following conclusions is definitely FALSE?

Accepted Answer

From P ≥ Q > R, we have P ≥ Q > R > S (since S ≤ R). T < Q means T is below Q. U = P means U ≥ Q > R. The statement 'S > T' cannot be confirmed because S ≤ R and T < Q, but their relationship is indeterminate. However, 'T ≥ R' is definitely FALSE because T < Q and Q > R does not guarantee T ≥ R; in fact, T could be less than R.

Question 14

Given: X ≤ Y < Z, A > Z, B ≥ X, and C = Z.
Which of the following conclusions is definitely TRUE?

Accepted Answer

From the inequalities: X ≤ Y < Z < A and B ≥ X and C = Z. Therefore, A > C is definitely true because A > Z and C = Z, so A > C.

Question 15

Given: A > B ≥ C, D < C, E ≤ B, and F = A.
Which of the following conclusions is definitely TRUE?

Accepted Answer

From the given inequalities: A > B ≥ C > D (since D < C), and E ≤ B, F = A. Therefore A = F is definitely true. Option D is correct.

Question 16

Consider:
X ≤ Y < Z
A > Z
B ≤ X
C > Y

Which conclusion is DEFINITELY TRUE?

Accepted Answer

This question tests transitive reasoning with mixed inequality types (≤, <, >) and the ability to identify definite conclusions.

Question 17

Given:
J ≤ K < L
M > L
N ≥ J
O < J
P ≤ N

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to identify the one conclusion that must logically follow from a complex set of inequalities involving six variables.

Question 18

Study the following statements carefully and determine which conclusion logically follows:

Statements:
1. A > B ≥ C
2. C > D
3. E ≤ B
4. D ≥ F
5. F > G

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

Let us trace through the relationships systematically:

From Statement 1: A > B ≥ C
- This means: A > B AND B ≥ C, so A > C and A > B

From Statement 2: C > D
- Combined with above: A > B ≥ C > D, so A > D

From Statement 3: E ≤ B
- E is at most equal to B

From Statement 4: D ≥ F
- Combined with C > D: C > D ≥ F, so C > F

From Statement 5: F > G
- Combined with above: C > F > G, so C > G and A > G

Now let's evaluate each option:

Option A (E > D): E ≤ B and B ≥ C > D. We know E ≤ B, but B could equal C, and C > D. However, E could be much smaller than D. For example: A=10, B=8, C=8, D=5, E=6, F=4, G=2. Here E=6 > D=5. But also: A=10, B=8, C=8, D=7, E=7, F=6, G=5. Here E=7 is not > D=7. NOT DEFINITELY TRUE.

Option B (A > G): From our chain: A > B ≥ C > D ≥ F > G. Therefore A > G is DEFINITELY TRUE.

Option C (E ≥ D): We established E ≤ B ≥ C > D. E could be less than D. NOT DEFINITELY TRUE.

Option D (F = G): F > G explicitly from Statement 5. F ≠ G. FALSE.

The answer is B.

Question 19

Given the following relationships:
A > B ≥ C > D
E ≤ C
F > A

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to chain inequalities and identify what must logically follow from given constraints.

Question 20

Consider:
X ≥ Y > Z
A < Z
B ≤ Y
C > X
D = B

Which of the following is INDETERMINATE (cannot be determined as true or false)?

Accepted Answer

This question requires identifying a relationship that cannot be conclusively proven true or false from the given constraints.

SSC CHSL Statement & Conclusions

Statement & Conclusions— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Statement & Conclusions — Practice Questions

60-Second Revision — Statement & Conclusions