Directions : In these questions symbols ©, #, %, $ and @ are used with…
2022
Directions : In these questions symbols ©, #, %, $ and @ are used with different meanings as follows.
‘M © N’ means ‘M is smaller than N’
‘M # N’ means ‘M is either smaller than or equal to N’
‘M % N’ means ‘M is greater than N’ ‘M $ N’ means ‘M is either greater than or equal to N’
‘M @ N’ means ‘M is neither smaller than nor greater than N’
In each of the following questions assuming the given statements to be true, find out which of the three conclusions I, II and III given below them is/are definitely true. Give answer
Statements:
L # M © N @ O % P; N $ Q @ T; G # H © T
Conclusions:
I. O $ Q
II. P % G
III. H © L
- A.
Both I and II
- B.
Only III
- C.
Both I and III
- D.
All I, II and III
- E.
Only I
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
In a coded-inequality problem each symbol is a fixed comparison relation. First decode every symbol, then build one combined chain of inequalities. A conclusion is definitely true only if it follows from the chain by an unbroken sequence of compatible relations; if the chain leaves two terms unlinked (or links them in a direction the conclusion contradicts), the conclusion is not definitely true.
Key rule for chaining: a strict "<" anywhere in a path forces the overall relation to be strict, while "=" links pass the relation through unchanged. "A ≥ B" together with "B = C" gives "A ≥ C".
Decode the symbols
© → smaller than (<)
# → smaller than or equal to (≤)
% → greater than (>)
$ → greater than or equal to (≥)
@ → neither smaller nor greater, i.e. equal (=)
Translate the statements
L # M © N @ O % P → L ≤ M < N = O > P
N $ Q @ T → N ≥ Q = T, so N ≥ Q and N ≥ T
G # H © T → G ≤ H < T
Evaluate each conclusion
I. O $ Q (is O ≥ Q ?)
From N = O and N ≥ Q we get O = N ≥ Q, hence O ≥ Q. The "≥" relation is exactly satisfied, so this conclusion holds. Definitely true.
II. P % G (is P > G ?)
P sits below N (N > P), and G ≤ H < T = Q ≤ N, so G also lies at or below N. Both P and G are bounded above by N, but no statement connects P and G directly, so their order is undetermined — P could be larger, smaller, or equal to G. Not definitely true.
III. H © L (is H < L ?)
H satisfies H < T ≤ N, and L satisfies L < N; both lie below N, but the chain provides no path linking H and L to each other. Their relative order cannot be fixed. Not definitely true.
Cross-check
Only conclusion I can be derived from an unbroken chain (O = N ≥ Q). II and III each require comparing two terms that the statements never connect, so a valid arrangement can make either of them false. Therefore exactly one conclusion — the relation O ≥ Q — is definitely true.