Reasoning: Inequalities Set 4

Directions (1 – 5): In the following questions, the symbols @, #, %, $ and © are used with the following meaning as illustrated below:
‘P@Q’ means ‘P is neither smaller than nor equal to 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 not smaller than Q’.
‘P©Q’ means ‘P is neither smaller than nor greater than Q’.

In each of the following questions, mark answer according to above symbols and their meaning.

1. Which of the following does not make P @ S and V # S definitely not true?
   A) P @ Q © R $ S $ T @ U © V
   B) P $ Q @ R @ V # T © S % U
   C) P # Q % R © S $ T © U $ V
   D) P © Q @ R © S @ T $ U © V
   E) None of these
   
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    Option C
   Check all the options. And find in which both P > S and V < S are false
   In C option, P < Q ≤ R = S ≥ T = U ≥ V. In this P < S and V ≤ S  
2. What will come in place of blank in following below such that both P @ S and V % R are definitely true?
   P $ Q @ R _ S $ T © U $ V
   i) @
   ii) ©
   iii) %
   iv) $
   A) Only (i)
   B) Either (i) or (iii)
   C) Either (i) or (ii) or (iv)
   D) Either (ii) or (iv)
   E) All are true
    
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     Option D
   With option D we get,
   P ≥ Q > R ≥ S ≥ T = U ≥ V OR P ≥ Q > R = S ≥ T = U ≥ V
   With both these we get, P > S and V ≤ R definitely true
3. Which of the following makes C $ E or B % E definitely true?
   A) A © B $ C @ D % E # F
   B) A # B % C $ D @ E # F
   C) A # B © C % D % E $ F
   D) A @ B % C © D # E @ F
   E) None of these
   
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     Option C
   Check all the options and find in which both or at least one of B ≤ E and C ≥ E is true. (because or is given)
   In C) option B ≤ E  is true. In all other options, both are false.
4. If “A % B # C © D @ E © F $ G” is true then which of the following is definitely not true?
   (i) A # D
   (ii) C © F
   (iii) B @ D
   (iv) E % G
   A) Only (i)
   B) Only (ii) and (iv)
   C) Only (ii) and (iii)
   D) Only (i), (iii) and (iv)
   E) All are true
   
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     Option B
   In A % B # C © D @ E © F $ G,
   A < D so A # D is true
   C > D so C © F is false (means not true)
   We do not have sufficient information about B and D to know relationship, so B @ D cannot be said definitely not true.
   E ≥ G so E % G is definitely false or not true  
5. Which of the following makes A $ C and E # B definitely true?
   A) A $ B $ C @ D % E # F
   B) A $ D $ B @ C @ E # F
   C) A © B # C % D @ E $ F
   D) A © B $ D © C @ E @ F
   E) None of these
   
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    Option D
   In D option both A $ C and E # B are true

Direction (6-10): Relationship between different elements is shown in the statements. Find if the conclusions also follow or not.

6. Statements: P >A ≤ R > S = T; U > R = V ≤ C; S > D ≥ E
   Conclusions:
   I. E ≤ C
   II. T > D
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
    
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   Option B
   E < S < R ≤ C so E < C
   T = S > D so T > D
7. Statements: A= B ≥ P < T = S; Q > C = D < P < U; E > F < U = V
   Conclusions:
   I. V > C
   II. A > Q
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
    
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   Option A
   V = U > C So V > C
   A ≥ P > D = C < Q, so relation between A and Q
8. Statements: P ≥ B = A ≥ S < T = Q; C = S > D > R = J
   Conclusions:
   I. C ≤ P
   II. Q > R
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
    
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   Option E
   
9. Statements: T ≤ S < Q < A = P ≥ M = K; R = D ≥ A ≥ C > S < B = C
   Conclusions:
   I. K < Q
   II. D > T
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
    
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   Option B
   
10. Statements: P > A ≤ R > S = T; U > R = V ≤ C; S > D ≤ E
    Conclusions:
    I. U ≥ E
    II. U < E
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow
     
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    Option C
    U > R > S > D ≤ E, so there is no relationship between U and E. But U will be certainly equal to, or greater than, or lesser than E. So these all three symbols are present in options. U ≥ E and U < E. SO eother of them will follow.