In a coded inequality, if ‘A @ B’ means ‘A is neither smaller than nor equal to B’, which of the following is true?
A is greater than B
For any two numbers A and B, exactly one of three relations holds: A < B, A = B or A > B.
‘A @ B’ rules out two of them: A is not smaller than B (so A < B is false) and A is not equal to B (so A = B is false).
The only remaining possibility is A > B, so the relation is fully determined and ‘cannot say’ does not apply.
Hence, A is greater than B.
Important Questions from Coded Inequalities
In the following questions, the symbols $, #, @, % and * illustrate the following meanings.
- P $ Q - P is not smaller than Q
- P # Q - P is neither greater than nor equal to Q.
- P @ Q - P is neither smaller than nor equal to Q.
- P % Q - P not greater than Q
- P * Q - P is neither greater than nor smaller than Q
Statements:
K # L, L % M, M * N, N # O
Conclusions:
I. K # M
II. K * M
III. L % O
Statements:
R @ S @ T © U © X; T $ V $ W
Conclusions:
I. R © X
II. X $ W
Statements:
E # F $ G $ H; G @ I
Conclusions:
I. H © I
II. E @ I
Statement: S @ T $ Q + R; Q * P @ W
Conclusion:
I) R # W
II) W $ R
Statement: S @ T $ Q + R; Q * P @ W
Conclusion:
I) R # W
II) W $ R
III) R @ T
