Reasoning Equality And InequalityPage 4

Section-4
Direction: In the following questions, the symbols @, $, #, * and % are used with the following meaning as illustrated below.
'A @ B' means 'A is not smaller than B'.
'A * B' means 'A is neither greater than nor equal to B'.
'A % B' means 'A is neither smaller than nor equal to B'.
'A # B' means 'A is not greater than B'.
'A $ B' means 'A is neither greater than nor smaller than B'.
Now, in each of the following questions, assuming the given statements to be true, find which of the four conclusions 1, 2, 3 and 4 given below them is/are definitely true and give your answer accordingly.

1.

Statements:
A # B, B % C, C * D
Conclusions:
1. C @ A
2. A # D
(a)If only Conclusion 1 follows
(b)If only Conclusion 2 follows
(c)If either Conclusion 1 or 2 follow
(d)If neither conclusion 1 nor 2 follows
Answer is: AAnswer is: A
A ≤ B . . . . . . (1)
B = C . . . . . . (2)
C < D . . . . . . (3)
Combining these, we get
A ≤ B = C < D
Hence C ≥ A and 1 follows.
Next, A < D and hence 2 (A ≤ D) does not follow.

2.

Statements:
P $ Q; Q @ S; S % R
Conclusions:
1. P @ R
2. R $ Q
(a)If only Conclusion 1 follows
(b)If only Conclusion 2 follows
(c)If either Conclusion 1 or 2 follow
(d)If neither conclusion 1 nor 2 follows
Answer is: DP > Q …….(1)
Q ≥ S ……(2)
S = R ……(3)
Combining these, we get
P > Q ≥ S = R
Hence P > R and 1 (P ≥ R) does not follow.
Also, R ≤ Q and 2 (R > Q) does not follow.

3.

Statements:
W * X; X # Y; Y $ Z
Conclusions:
1. W * Z
2. W @ Z
(a)If only Conclusion 1 follows
(b)If only Conclusion 2 follows
(c)If either Conclusion 1 or 2 follow
(d)If neither conclusion 1 nor 2 follows
Answer is: CW < X ……..(1)
X ≤ Y ….. ..(2)
Y > Z ……..(3)
Combining these, we get W < X ≤ Y > Z.
Hence W and Z can't be compared but either 1 (W < Z) or (W ≥ Z) must follow as they form a complementary pair.

4.

Statements:
G @ H; H $ J; J % K
Conclusions:
1. K * G
2. J * G
(a)If only Conclusion 1 follows
(b)If only Conclusion 2 follows
(c)If either Conclusion 1 or 2 follow
(d)If both conclusions 1 and 2 follow
Answer is: DG ≥ H …….(1)
H > J ……..(2)
J = K ……..(3)
Combining these, we get
G ≥ H > J = K.
Hence K < G and 1 follows.
Also, J < G and 2 follow.

5.

Statements:
N @ M; M $ P; P # T
Conclusions:
1. T # N
2. P * N
(a)If only Conclusion 1 follows
(b)If only Conclusion 2 follows
(c)If either Conclusion 1 or 2 follow
(d)If both conclusions 1 and 2 follow
Answer is: BN ≥ M ……..(1)
M > P …….(2)
P ≤ T ……...(3)
From equation 1 and 2,
N ≥ M > P or N > P ……..(4)
Hence P < N and 2 follows.
From equation 3 and 4, However, T and N can't be compared.
Hence 1 does not follow.

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