Inequality questions with solutions

1. Question 1Easy

   Statements: D ≤ C ≥ B ≤ F Conclusions: I. B ≤ C II. F < C Which conclusion(s) definitely follow?

   • A.Only I followsCorrect
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is true and conclusion II is not necessarily true. Hence: only i follows.

2. Question 2Easy

   Statements: E < D ≤ B = F Conclusions: I. B ≥ D II. B > F Which conclusion(s) definitely follow?

   • A.Only I followsCorrect
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is true and conclusion II is not necessarily true. Hence: only i follows.

3. Question 3Easy

   Statements: B ≥ A < D > F Conclusions: I. D ≥ F II. A ≥ B Which conclusion(s) definitely follow?

   • A.Only I followsCorrect
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is true and conclusion II is not necessarily true. Hence: only i follows.

4. Question 4Easy

   Statements: B ≤ E = A ≤ D Conclusions: I. E ≤ B II. B ≤ D Which conclusion(s) definitely follow?

   • A.Only I follows
   • B.Only II followsCorrect
   • C.Both I and II follow
   • D.Neither I nor II follows
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is not necessarily true and conclusion II is true. Hence: only ii follows.

5. Question 5Easy

   Statements: P > Q >= R = S < T Conclusions: I. P > S II. T > R

   • A.Only conclusion I follows
   • B.Only conclusion II follows
   • C.Both conclusions followCorrect
   • D.Neither conclusion follows
   • E.Either conclusion I or II follows
   Show solution

   From P > Q >= R = S, P is strictly greater than S, so conclusion I holds. From R = S < T, T is greater than S, and since R equals S, T is greater than R, so conclusion II holds. Both follow.

6. Question 6Easy

   In the expression A > B ≥ C = D, which of the following is definitely true?

   • A.A > DCorrect
   • B.B < D
   • C.C > A
   • D.A = C
   Show solution

   A > B, B ≥ C and C = D, so A is greater than B which is at least C which equals D. Therefore A > D is definitely true.

7. Question 7Easy

   Given the statement P > Q >= R and R > S, which of the following is definitely true?

   • A.P > SCorrect
   • B.Q = S
   • C.S >= Q
   • D.R >= P
   • E.None of these is definitely true
   Show solution

   Chain the relations: P > Q, Q >= R and R > S give P > Q >= R > S. A chain of this kind is valid as long as every link points the same way, and the weakest link decides the result. Since at least one strict inequality appears between P and S, P > S is definite. Q = S is impossible because Q is strictly greater than S, and options C and D reverse the chain.

8. Question 8Easy

   Statements: E ≤ C ≤ B = F Conclusions: I. E < B II. B ≤ C Which conclusion(s) definitely follow?

   • A.Only I follows
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II followsCorrect
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is not necessarily true and conclusion II is not necessarily true. Hence: neither i nor ii follows.

9. Question 9Easy

   Statements: B < E ≥ A ≤ C Conclusions: I. E > A II. C < A Which conclusion(s) definitely follow?

   • A.Only I follows
   • B.Only II follows
   • C.Both I and II follow
   • D.Neither I nor II followsCorrect
   • E.Either I or II follows
   Show solution

   Reading the chain, conclusion I is not necessarily true and conclusion II is not necessarily true. Hence: neither i nor ii follows.

10. Question 10Easy

    Statements: E < C > A > B Conclusions: I. B < E II. A ≥ E Which conclusion(s) definitely follow?

    • A.Only I follows
    • B.Only II follows
    • C.Both I and II follow
    • D.Neither I nor II followsCorrect
    • E.Either I or II follows
    Show solution

    Reading the chain, conclusion I is not necessarily true and conclusion II is not necessarily true. Hence: neither i nor ii follows.

11. Question 11Easy

    Statements: F = B > A < C Conclusions: I. B > F II. A ≤ F Which conclusion(s) definitely follow?

    • A.Only I follows
    • B.Only II followsCorrect
    • C.Both I and II follow
    • D.Neither I nor II follows
    • E.Either I or II follows
    Show solution

    Reading the chain, conclusion I is not necessarily true and conclusion II is true. Hence: only ii follows.

12. Question 12Easy

    Statements: C ≤ E ≥ A < D Conclusions: I. D ≥ A II. E ≤ C Which conclusion(s) definitely follow?

    • A.Only I followsCorrect
    • B.Only II follows
    • C.Both I and II follow
    • D.Neither I nor II follows
    • E.Either I or II follows
    Show solution

    Reading the chain, conclusion I is true and conclusion II is not necessarily true. Hence: only i follows.

These are 12 of 130 inequality questions in the bank. Attempt the rest with instant feedback in the practice drills, or under a clock in the mock tests.