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Coded Inequalities Test 1
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Coded Inequalities Test 1

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  • Question 1/10
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    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

    Solutions

    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).

  • Question 2/10
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    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

    Solutions

    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)

  • Question 3/10
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    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

    Solutions

    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.

  • Question 4/10
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    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

    Solutions

    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)

  • Question 5/10
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    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

    Solutions

    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.

  • Question 6/10
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    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

    Solutions

    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.

  • Question 7/10
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    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

    Solutions

    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.

  • Question 8/10
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    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

    Solutions

    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.

  • Question 9/10
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    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

    Solutions

    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).

  • Question 10/10
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    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

    Solutions

    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.

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