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Inequality Test 2
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Inequality Test 2

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  • Question 1/10
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    Directions For Questions

    DIRECTIONS: In the following questions, the symbols @, #,% , © and * are used with the following meanings:

    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.

    ...view full instructions

    Choose correct answer as given in options.

    Statements:

    Q # R, T*L, R*M, L%Q

    Conclusions: 

    I. M © T

    II. T*R

    Solutions

    Statements: 

    Q = R, T<L, R<M, L<Q

    T<L<Q=R<M

    Conclusions: 

    I. M > T        (true)

    II. T<R         (true)

    Hence, both I and II are true.

  • Question 2/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols @, #,% , © and * are used with the following meanings:

    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.

    ...view full instructions

    Choose correct answer as given in options.

    Statements: 

    Z*N, D%G,  B*Z, D # N

    Conclusions: 

    I. G © Z

    II. N*B

    Solutions

    Statements: 

    Z<N, D<G,  B<Z, D = N

    B<Z<N=D<G

    Conclusions: 

    I. G > Z           (true)

    II. N<B            (false)

    Hence, only conclusion I is true.

  • Question 3/10
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    Directions For Questions

    DIRECTIONS: In the following questions, the symbols #, $, @, % and © are used with the following meaning as illustrated below:

    ‘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’.

    ...view full instructions

    Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? 

    Statements:

    J % D, Q # D, Q @ M

    Conclusions:

    I. Q © J

    II. Q $ J

    Solutions

    (i) P # Q means P < Q.

    Therefore P > Q or P = Q  Thus P ≥ Q

    (ii) P $ Q means P< Q and P > Q. Therefore P = Q

    (iii) P @ Q means P > Q and P ≠ Q. Therefore P < G

    (iv) P % Q means P > Q. Therefore P < Q or P = Q. Thus P ≤ Q

    (v) P © Q means P < Q and P ≠ Q. Therefore P > Q. Thus,

    P ≠ Q ⇒ ≥

    P $ Q ⇒ =

    P @ Q ⇒ <

    P % Q ⇒ ≤ 

    P © Q ⇒ >

    Statements

    J % D ⇒ J ≤ D

    Q # D ⇒ Q ≥ D

    Q @ M ⇒ Q < M

    Therefore J ≤ D ≤ Q < M

    Conclusions

    I.Q @ J ⇒ Q > J        (False)

    II. Q $ J ⇒ Q = J       (False)

  • Question 4/10
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    Directions For Questions

    DIRECTIONS: In the following questions, the symbols #, $, @, % and © are used with the following meaning as illustrated below:

    ‘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’.

    ...view full instructions

    Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? 

    Statements:

    B $ K, K @ D, D # M

    Conclusions:

    I. B $ M 

    II. B @ M

    Solutions

    (i) P # Q means P < Q.

    Therefore P > Q or P = Q  Thus P ≥ Q

    (ii) P $ Q means P< Q and P > Q. Therefore P = Q

    (iii) P @ Q means P > Q and P ≠ Q. Therefore P < G

    (iv) P % Q means P > Q. Therefore P < Q or P = Q. Thus P ≤ Q

    (v) P © Q means P < Q and P ≠ Q. Therefore P > Q. Thus,

    P ≠ Q ⇒ ≥

    P $ Q ⇒ =

    P @ Q ⇒ <

    P % Q ⇒ ≤ 

    P © Q ⇒ >

    Statements  

    B $ K ⇒ B = K

    K @ D ⇒ K < D

    D # M ⇒ D ≥ M

    Therefore  B = K < D ≥ M

    Conclusions

    I. B $ M  ⇒ B = K            (False)

    II. B @ M  ⇒ B < M         (False)

  • Question 5/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols #, $, @, % and © are used with the following meaning as illustrated below:

    ‘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’.

    ...view full instructions

    Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? 

    Statements:

    F # G, N $ G, N © T

    Conclusions:

    I. T © F   

    II. N % F

    Solutions

    (i) P # Q means P < Q.

    Therefore P > Q or P = Q  Thus P ≥ Q

    (ii) P $ Q means P< Q and P > Q. Therefore P = Q

    (iii) P @ Q means P > Q and P ≠ Q. Therefore P < G

    (iv) P % Q means P > Q. Therefore P < Q or P = Q. Thus P ≤ Q

    (v) P © Q means P < Q and P ≠ Q. Therefore P > Q. Thus,

    P ≠ Q ⇒ ≥

    P $ Q ⇒ =

    P @ Q ⇒ <

    P % Q ⇒ ≤ 

    P © Q ⇒ >

    Statements

    F # G ⇒ F ≥ G

    N $ G ⇒ N = G

    N © T ⇒ N > T

    Therefore F ≥ G = N > T

    Conclusions

    I. T © F  ⇒ T > G             (False)

    II. N % F  ⇒ N ≤ F           (True)

  • Question 6/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols #, $, @, % and © are used with the following meaning as illustrated below:

    ‘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’.

    ...view full instructions

    Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? 

    Statements:

    M © R, R @ K, K $ T

    Conclusions:

    I. T © R

    II. T © M

    Solutions

    (i) P # Q means P < Q.

    Therefore P > Q or P = Q Thus P ≥ Q

    (ii) P $ Q means P< Q and P > Q. Therefore P = Q

    (iii) P @ Q means P > Q and P ≠ Q. Therefore P < G

    (iv) P % Q means P > Q. Therefore P < Q or P = Q. Thus P ≤ Q

    (v) P © Q means P < Q and P ≠ Q. Therefore P > Q. Thus,

    P ≠ Q ⇒ ≥  

    P $ Q ⇒ =

    P @ Q ⇒ <

    P % Q ⇒ ≤ 

    P © Q ⇒ >

    Statements

    M © R ⇒ M > R

    R @ K ⇒ R < K

    K $ T ⇒ K = T

    Therefore M > R < K = T

    Conclusions

    I. T © R ⇒ T > R            (True)  

    II. T © M ⇒ T > M           (false)

  • Question 7/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols *,©,=,@, and # and are used with the following meaning:

    P * Q means P is greater than Q.

    P © Q means P is either greater than or equal to Q.

    P = Q means P is equal to Q.

    P @ Q means P is smaller than Q.

    P # Q means P is either smaller than or equal to Q.

    ...view full instructions

    Choose correct answer as given in options.

    Statements: M @ L, O * P, M = N, O # N

    Conclusions: I. M * O   II. M = O

    Solutions

    Statements: 

    M < L, O > P, M = N, O < N

    P < O < N = M < L

    Conclusions:

    I. M > O              (may be)

    II. M = O             (may be)

    Either conclusion I or conclusion II is true.

  • Question 8/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols *,©,=,@, and # and are used with the following meaning:

    P * Q means P is greater than Q.

    P © Q means P is either greater than or equal to Q.

    P = Q means P is equal to Q.

    P @ Q means P is smaller than Q.

    P # Q means P is either smaller than or equal to Q.

    ...view full instructions

    Choose correct answer as given in options.

    Statements: W @ N, S = Q, R © N, S @ R

    Conclusions: I. W @ R   II. N = Q

    Solutions

    Statements: 

    W < N, S = Q, R > N, S < R

    W < N < R

    Q = S < R

    Conclusions: 

    I. W < R                 (true)

    II. N = Q                (false)

    Only conclusion I is true.

  • Question 9/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols *,©,=,@, and # and are used with the following meaning:

    P * Q means P is greater than Q.

    P © Q means P is either greater than or equal to Q.

    P = Q means P is equal to Q.

    P @ Q means P is smaller than Q.

    P # Q means P is either smaller than or equal to Q.

    ...view full instructions

    Choose correct answer as given in options.

    Statements: A @ B, D @ E, C = D, C © B

    Conclusions: I. E * B   II. B = E

    Solutions

    statements: 

    A < B, D < E, C = D, C > B

    A < B < C = D < E

    Conclusions:  

    I. E > B                (true)  

    II. B = E               (false)  

    Only conclusion I is true.

  • Question 10/10
    1 / -0

    Directions For Questions

    DIRECTIONS: In the following questions, the symbols *,©,=,@, and # and are used with the following meaning:

    P * Q means P is greater than Q.

    P © Q means P is either greater than or equal to Q.

    P = Q means P is equal to Q.

    P @ Q means P is smaller than Q.

    P # Q means P is either smaller than or equal to Q.

    ...view full instructions

    Choose correct answer as given in options.

    Statements: W * U, Y = X, Z @ Y, X © W 

    Conclusions: I. Z = W   II. X * Z

    Solutions

    Statements: 

    W > U, Y = X, Z < Y, X > W

    Y = X > W > U 

    X = Y > Z

    Conclusions: 

    I. Z = W             (false)

    II. X > Z             (true)

    Only conclusion II is true.

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