   ### Reasoning Questions based on Symbols

REASONING ABILITY – 2
Questions based on symbols.

In this section there are many different types of questions. One of the type is where a lot of symbols are used having different meanings and then questions are framed on the basis of the inference of these symbols. The questions are very easy and scoring if you can quickly decode and understand the meaning of the symbols. Below are some questions where hardly any knowledge of maths is used but you must have a deep sense of understanding basics otherwise you will end up making mistakes like. If I tell I> J ; & J = M ; & M< N and N < P; Now if I ask you relation between I J M N & P, It would sound a bit cumbersome, but if you look at it with relax mind then you can observe that I is greater than J which is equal to M so indirectly I is also greater than M and since M is less than N so indirectly I is also greater than N, But P is greater than N; How much greater ? We don't know. May be just a little greater so that it is still less than all the remaining ones or may be so greater that it is the greatest. In other words the extent to which P is more than N is not told here in this statement. So these are the things you need to keep in mind. Rest is all very very easy !!

In the following questions, the symbol  × , ∂ , % ,   © , @ , are used with the following illustrations.

P % Q means P is not smaller than Q
P © Q means P is neither smaller than nor equal to Q
P x 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 greater than nor smaller than Q

Question  1    Statement – R K ; K x M ; M @ J

Conclusions -:

III.  R  x J

A. Only  I & I are true
B. Only II & III are true
C. Only I & III are true.
D. All I, II & III are true
E. None of these

Question 2    Statements –  Z @ M ; M © K ; K X F

Conclusions - :
II.   K X Z
a. None is true
b. Only I is true
c. Only II is true
d. Only III is true
e. Only II & III are true.

Question – 3 Statements – V % H ; H @ F ; F ∂ E

Conclusions :-
I.     F @ V
II.   F X V
III.  E % H
a. Only either I or II is true
b. Only III is true
c. Only I & II are true
d. All I, II & III are true.
e. Only either I or II and three are true.

Question – 4 -    Statements – W ©  T ; T ∂ N ; N % D

Conclusions :-
I.     D X T
III.  D @ T
a. None in True
b. Only I is true
c. Only II is true
d. Only III is true
e. Only I & II are true

Solutions -  First we must understand what actually the symbols imply.

P % Q means P is not smaller than Q -----------------  [ P≥ Q ]
P © Q means P is neither smaller than nor equal to Q ---  [ P > Q }
P x Q means P is neither greater than nor equal to Q --------- [ P < Q ]
P Q means P is not greater than Q ---------- [  P ≤  Q  ]
P @ Q means P is neither greater than nor smaller than Q------- [ P=Q ]

Answer – 1 -  Statement – R K ; K x M ; M @ J

Means = R ≤ K < M = J

Conclusions -:
I.     J ©  K -------    [  J > K ]
II.   M © R ----    [  M > R ]
III.  R  x J  ------    [  R < J  ]
Clearly All the conclusions are true

Answer – 2 - Statements –  Z @ M ; M © K ; K X F

Means  Z = M  > K  < F

Conclusions - :
I.     F © Z ----------  [ F > Z ] cannot be said.
II.   K X Z ---------   [ K < Z ] Surely it is
III.  F © M --------    [ F > M ] cannot be said
So Only II is correct.

Answer – 3- Statements – V % H ; H @ F ; F ∂ E

Means – V ≥ H = F ≤ E

Conclusions :-
I.     F @ V ----    [ F=V ] not sure may nor may not be
II.   F X V ---------   [ F < V ] Not sure may or may not be
III.  E % H ------- [ E ≥ H ] Surely.
But here F= H & H ≤ V so indirectly F≤V so either F= V or F < V but not both at a time, but atleast one has to hold. So either I or II should be there and III is always right. So answer is either I or II  & III are correct.

Answer – 4 - Statements – W ©  T ; T ∂ N ; N % D

Means – W > T
N ≥ T
N ≥ D

Conclusions :-
I.     D X T  -----  [ D < T ] cannot be said. No idea of relation between them
II.   W © N -- [ W > N ] cannot be said
III.  D @ T -- [ D = T ]  cannot be said.
So here None is true.