Symbol notations inequalities questions

Download Handout 1 on Symbols and Operations – Must do 60 EASY questions>>
Download Handout 2 Symbol inequalities questions РMust do 36 MEDIUM questions>>

 

Symbols and Operations

Below are four problems dealing with the relationship between different elements.

Directions to solve:

If,
i) A @ B means A is greater than B;
ii) A * B means A is either greater than or equal to B;
iii) A # B means A is equal to B;
iv) A $ B means A is either smaller than or equal to B;
v) A + B means A is smaller than B.

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?

Give answer (a) if only conclusion I is true
Give answer (b) if only conclusion II is true
Give answer (c) if either conclusion I or II is true
Give answer (d) if neither conclusion I nor II is true.
Give answer (e) if both conclusions I and II are true.

Question 1

Statements :

P * Q; Q $ R; S + T: R + S

Conclusions :

I. Q + S
II. Q + T

Options: a, b, c, d, e
Answer : option e.

Solution :

Given Statements: P * Q; Q $ R; S + T; R + S
Converting the statements as follows:
P * Q => P is greater than or equal to Q; i.e., P > = Q
Q $ R => Q is less than or equal to R; i.e., Q < = R
S + T => S is less than T; i.e., S < T
R + S => R is less than S; i.e., R < S

After conversion, combining the above, we have,

P > = Q < = R < S < T
From above inequality, we have, Q < = R < S < T
=> Q < S and Q < T

Given conclusions,

Q + S => Q < S which is true
Q + T => Q < T which is also true.

Hence, both conclusions I and II are true.

Question 2

Statements :

P + Q; R $ S; T * Q; R @ P

Conclusions :

I. P $ S
II. P + T

Options: a, b, c, d, e
Answer : option d.

Solution :

Given Statements: P + Q; R $ S; T * Q; R @ P;

Converting the statements as follows:

P + Q => P < Q
R $ S => R is less than or equal to S; i.e., R < = S
T * Q => T is greater than or equal to Q; i.e., T > = Q
R @ P => R > P

Combining the above four, we get, S > = R > P < Q < = T
From the above inequality, we have
S > P and P < T ….(1)

Given conclusions,
S $ P => S < = P which is not true since S > P
P + T => P < T which is true.

Hence, conclusion II is true.

Question 3

Statements :

P + Q; R $ S; S * T; T @ P

Conclusions :

I. S $ P
II. R $ T

Options: a, b, c, d, e
Answer : option d.

Solution:

Given Statements P + Q; R @ S; S * T; T @ P

Converting the statements as follows:
P + Q => P < Q
R @ S => R is greater than S; i.e., R > S
S * T => S is greater than or equal to T; i.e., S > = T
T @ P => T > P

Combining above four statements, we get R > S > = T > P < Q
From above inequality, we have
S > = T > P; i.e.,S > P
R > S > = T => R > T

Given conclusions:
S $ P means S < = P which is not true since S > P.
R $ T means R < = T which is not true since R > T.

Hence, neither conclusion I nor II is true.

Question 4

Statements :

P * Q; R $ S; S # P; R @ T

Conclusions :

I. T @ S
II. S * Q

Options: a, b, c, d, e
Answer : option b.

Solution :

Given statements: P * Q; R $ S; S # P; R @ T
Converting the statements as follows:
P * Q => P is greater than or equal to Q; i.e., P > = Q
R $ S => R is less than or equal to S; i.e., R < = S
S # P => S is equal to P; i.e., S = P
R @ T => R is greater than T; i.e., R > T

After conversion, combining the above, we have,
T < R < = S = P > = Q

From the above inequality, we have,
T < S and S > = Q.

Given conclusions,

T @ S => T > S which is not true since T < S
S * Q => S > = Q which is true.

Hence, only conclusion II is true.

Download Handout >>

One thought on “Symbol notations inequalities questions

  • Sir / Ma’am,
    I need to know, where can i study for general awareness section of Snap 2016. As there is 6 days remaining for the exam, what sources can I use to study for General Awareness, please guide me on this.

Leave a Reply

Your email address will not be published.