Mathematical operation and symbol notation


Direction: In these questions, relationship between different elements is shown in the statements. These statements are followed by two conclusions.

  1. Statements
    B < C, D > B, C > K, K ≤ N, N < B
    Conclusions
    I. C > N
    II. B > K
    1. Only Conclusion I follows
    2. Only Conclusion II follows
    3. either Conclusion I or II follows
    4. neither Conclusion I nor II follows
    5. both Conclusion I and II follow

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    Conclusion
    I. C > N         (✔)
    II. B > N           (✔)

    Correct Option: D

    Conclusion
    I. C > N         (✔)
    II. B > N           (✔)


Direction: In these questions, relationships between different elements is shown in the statement. The statement is followed by two conclusions. Study the conclusions based on the given statement and select the appropriate answer.

  1. Statement ::
    K ≥ L > M ≥ N
    Conclusions ::
    I. N ≤ K
    II. N < K
    1. Both Conclusion I and II follow
    2. Neither Conclusion I nor II follows
    3. Either Conclusion I or II follows
    4. Only Conclusion I follows
    5. Only Conclusion II follows

  1. View Hint View Answer Discuss in Forum

    K ≥ L > M ≥ N
    Conclusions
    I. N ≤ K             (x)
    II. N < K            (✔)
    Thus, only Conclusion II follows.

    Correct Option: E

    K ≥ L > M ≥ N
    Conclusions
    I. N ≤ K             (x)
    II. N < K            (✔)
    Thus, only Conclusion II follows.



  1. Statement ::
    Z ≥ Y = W ≥ X
    Conclusions ::
    I. W < Z
    II. W = Z
    1. Only Conclusion II follows
    2. Only Conclusion I follows
    3. Neither Conclusion I nor II follows
    4. Either Conclusion I or II follows
    5. Both Conclusion I and II follow

  1. View Hint View Answer Discuss in Forum

    Z ≥ Y = W ≥ X
    Conclusions
    I. W < Z          (✔)
          or
    II. W = Z             (✔)
    Thus, either Conclusion I or II follows.

    Correct Option: D

    Z ≥ Y = W ≥ X
    Conclusions
    I. W < Z          (✔)
          or
    II. W = Z             (✔)
    Thus, either Conclusion I or II follows.


Direction: In the following questions, the symbols @, $, #, © and % are used with the following meanings as illustrated below.
'P $ Q' means 'P is not smaller than Q'.
'P © Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means 'P is neither smaller than nor equal to Q'.
'P % Q' means 'P' is not greater than Q'.
'P @ Q' means 'P is neither greater than nor smaller 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 given below them is/are definitely true and given your answer accordingly.

  1. Statements ::
    R # J, J $ D, D @ K, K % T
    Conclusions ::
    I. T # D
    II. T @ D
    III. R # K
    IV. J $ T
    1. Either I or II is true
    2. Only III is true
    3. III and IV are true
    4. Either I or II and III are true
    5. None of the above

  1. View Hint View Answer Discuss in Forum

    Statements
    R # J ⇒ R >J
    J $ D ⇒ J ≥ D
    D @ K ⇒ D = K
    K % T ⇒ K ≤ T
    i.e., R > J ≥ D = K ≤ T
    Conclusions
    I. T # D ⇒ T > D       (may be)
    II. T @ D ⇒ T = D          (may be)
    III. R # K ⇒ R > K           (✔)
    IV. J $ T ⇒ J ≥ T             (x)
    Hence, either conclusion I or II and III are definitely true.

    Correct Option: D

    Statements
    R # J ⇒ R >J
    J $ D ⇒ J ≥ D
    D @ K ⇒ D = K
    K % T ⇒ K ≤ T
    i.e., R > J ≥ D = K ≤ T
    Conclusions
    I. T # D ⇒ T > D       (may be)
    II. T @ D ⇒ T = D          (may be)
    III. R # K ⇒ R > K           (✔)
    IV. J $ T ⇒ J ≥ T             (x)
    Hence, either conclusion I or II and III are definitely true.



  1. Statements ::
    T % R, R $ M, M @ D, D © H
    Conclusions ::
    I. D % R
    II. H # R
    III. T © M
    IV. T % D
    1. Only I is true
    2. I and IV are true
    3. II and IV are ture
    4. II and IV are ture
    5. None of the above

  1. View Hint View Answer Discuss in Forum

    Statements
    T % R ⇒ T ≤ R
    R $ M ⇒ R ≥ M
    M @ D ⇒ M = D
    D © H ⇒ D < H
    i.e., T ≤ R ≥ M = D < H
    Conclusions
    I. D % R ⇒ D ≤ R         (✔)
    II. H # R ⇒ H > R          (x)
    III. T ©M ⇒ T < M         (x)
    IV. T % D ⇒ T ≤ D          (x)

    Correct Option: A

    Statements
    T % R ⇒ T ≤ R
    R $ M ⇒ R ≥ M
    M @ D ⇒ M = D
    D © H ⇒ D < H
    i.e., T ≤ R ≥ M = D < H
    Conclusions
    I. D % R ⇒ D ≤ R         (✔)
    II. H # R ⇒ H > R           (x)
    III. T ©M ⇒ T < M           (x)
    IV. T % D ⇒ T ≤ D          (x)

    Hence conclusion I is definitely true.