Dear Reader,
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.
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.
