Reasoning Questions (Inequality) for AAO and upcoming Exams 2016

    Reasoning Questions (Inequality) for AAO and upcoming Exams 2016
    Reasoning Questions (Inequality) for AAO and upcoming Exams 2016 Set-53:
    Dear Readers, Important Practice Reasoning Questions for Upcoming AAO Exams was given here with Explanations. Aspirants those who are preparing for the examination can use this.

    Directions (Q.1-5): In the following questions, the symbols =,>,>,< and< are used with the following meanings:

    P< Q means P is neither smaller than nor equal to Q
    P=Q means P is not smaller than Q
    P>Q means P is neither greater nor smaller than Q
    P> Q means P is neither greater than nor equal to Q
    P
    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.

    1).Statements: P = R, Y> T, U> V
    Conclusions: I.V> U                 II.Y = R
    a)  if only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If either conclusion I nor II is true
    e)  if both conclusions I and  II are true


    2).Statements: P< D, D> Z, D< X
    Conclusion: I.D> P                   II.P< Z
    a)  if only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If either conclusion I nor II is true
    e)  if both conclusions I and  II are true


    3).Statements: L> M, N = O, N> A
    Conclusions: N> M         II. O> M
    a)  if only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If either conclusion I nor II is true
    e)  if both conclusions I and  II are true


    4).Statements: P> H, Z< J ,  H> J
    Conclusions: I. J< P       II. Z< H
    a)  if only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If either conclusion I nor II is true
    e)  if both conclusions I and  II are true


    5).Statements: A> B, P> L, L = S
    Conclusions: I.B> L        II.L< B
    a)  if only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If either conclusion I nor II is true
    e)  if both conclusions I and  II are true


    Directions (6-10): In the following questions, the symbols ✡, !, #, $ and @ are used with the following meanings as illustrated below

    ‘R✡S’ means ‘R is not greater than S’
    ‘R!S ‘ means ‘R is neither greater than nor equal to S’
    ‘R#S’ means ‘R is not smaller than S’
    ‘R$S’ means ‘R is neither smaller nor greater than S’
    ‘R@S’ means R is neither smaller than nor equal to S
    Now, in each of the following questions, assuming the given statements to be true, find out which of the two conclusions I and II given below them is /are definitely true.

    6).Statements: P # S, S @ R, P ✡ N
    Conclusions: I. N $ R 
    II. P @ R
    a)  If only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If neither conclusion I nor II is true
    e)  If both conclusions I and II are true.


    7).Statements: N $ S, S @ R, R # Q, Q # T
    Conclusions: I. N @ R
                       II. R # T
    a)  If only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If neither conclusion I nor II is true
    e)  If both conclusions I and II are true.


    8).Statements: P ! S ,S # N, N @ R, P ! Q
    Conclusions: I. Q @ S
                          II. S @ R
    a)  If only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If neither conclusion I nor II is true
    e)  If both conclusions I and II are true.


    9).Statements: C $ D, D @ E, D ! G, C # P, P @ N
    Conclusions: I. D#P
                       II. C ! G
    a)  If only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If neither conclusion I nor II is true
    e)  If both conclusions I and II are true.


    10).Statements: Z $ R, R ✡ Q, Q # P, P ! K
    Conclusions: I. Z # Q
                           II. P ! Z
    a)  If only conclusion I is true
    b)  If only conclusion II is true
    c)  If either conclusion I or II is true
    d)  If neither conclusion I nor II is true
    e)  If both conclusions I and II are true.


    Answers:                    
    1). d)  2). e)  3). d)  4). e)  5). c)  6). b)  7). e)  8). b)  9). e)  10). d)

    EXPLANATIONS:

    1.P> R __________(i)
    Y< T_____________(ii)
    U< V_____________(iii)
    From (iii), conclusion I is not true. There is no information regarding the relation between Y and R. Hence II can not be concluded.
    Answer: d)

    2.P> D_______________(i)
    D = Z_________________(ii)
    D> X_________________(iii)
    From (i), D
    P> D = Z => P> Z. Hence II is also true.
    Answer: e)

    3.L> M________(i)
    N> O _________(ii)
    N< A__________(iii)
    There is no information regarding the relation either between N and M or between O and M. Hence both conclusions I and II are not necessarily true.
    Answer: d)

    4.P< H____________(i)
    Z> J_____________(ii)
    H< J______________(iii)
    Combining (i) and (iii), we get
    P< H< J ⇒ J> P. Hence conclusion I is true.
    Combining (ii) and (iii), we get
    Z> J> H ⇒ Z> H.
    Hence conclusion II is also true.
    Answer: e)

    5.A = B__________(i)
    P< L___________(ii)
    L> S___________(iii)
    There is no specific relation between B and L but both conclusions I and II make a complementary pair. Hence either I or II will be true.
    Answer: c)

    Questions (6-10):

    ✡ →< ! →<, # →>, $ → = and @ →>

    6.From the given statement, we get
    P # S ⇒ P> S_____________(i)
     S @ R ⇒ S> R____________(ii)
    P ✡ N ⇒ P< N_____________(iii)
    Combining (i), (ii), (iii) we get
    N> P> S> T
    Thus N> R. Hence Conclusion I (N = R) does not follow.
    Check for II. P> R. Hence conclusion II (P @ R) is true.
    Answer: b)

    7.From the given statement, we get
    N $ S ⇒ P = S______________(i)
    S @ R ⇒ S> R_____________(ii)
    R # Q ⇒ R> Q_____________(iii)
    Q # T ⇒ Q> T______________(iv)
    Combining (i), (ii)  (iii) and (iv),we get
    N = S> R> Q> T
    Now, check for I. N>R is true. Hence, conclusion I (N @ R) follows. Again, R> T. Hence, conclusion II (R # T) is true. Thus, both conclusions I and II follow.
    Answer: e)

    8.From the given statement, we get
    P ! S ⇒ P< S_________(i)
    S # N ⇒ S> N_________(ii)
    N @ R> N> R_________(iii)
    P ! Q ⇒ P< Q__________(iv)
    Combining (i), (ii), (iii) and (iv),we get
    Q> P< S> N> R
    Thus, we can’t compare Q and S. Hence, conclusion I (Q @ S) is not true.
    Again, S> R. Hence, conclusion II (S @ R) is true.
    Answer: b)

    9.From the given statement, we get
    C $ D ⇒ C = D___________(i)
    D @ E ⇒ D> E___________(ii)
    D ! G ⇒ D< G_____________(iii)
    C # P ⇒ C> P_____________(iv)
    P @ N ⇒ P> N_____________(v)
    Combining all these statements, we get
    N< P< C = D> E and N< P< C = D> G
    Thus, P< D or D> E and N< P< C = D> G
    Thus, P< D or D> P is true. Hence, conclusion I (D # P) is true. Again, C< G is true. Hence conclusion II (C ! G) is true.
    Answer: e)

    10.From the given statement, we get
    Z $ R ⇒ Z = R______________(i)
    Q # P ⇒ Q> P______________(ii)
    R ✡ Q ⇒ R< Q_______________(iii)
    P ! K ⇒ P< K__________________(iv)
    Answer: d)

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