Direction : Read the given information carefully and answer the questions…
2021
Direction : Read the given information carefully and answer the questions below:
1%2 means 2 is neither smaller nor greater than 1
1&2 means 2 is neither greater nor equal to 1
1*2 means 2 is neither smaller nor equal to 1
1$2 means 2 is not greater than 1
1α2 means 2 is not smaller than 1
Statements: U$LαK%T; W&P; D*J; W%R$L; M*TαJ
Conclusions: I. M*W
II. D&K
III. J$P
- A.
Both I and III are true
- B.
None is true
- C.
Only II is true
- D.
Only I is true
- E.
Both II and III are true
Show answer & explanation
Correct answer: B
Concept
In a coded-inequality problem each symbol stands for a fixed relation. First decode every symbol into a standard inequality (=, >, <, ≥, ≤). Then combine statements that share a letter into a single chain. A conclusion is definitely true only if a chain of statements FORCES its required direction for every consistent assignment. Two letters may well sit in the same network yet have no chain that pins their order — because the connecting path mixes opposing inequalities, or passes through a “≥/≤” bound that does not transmit a strict order. In that case the conclusion is not definite.
Decoding the symbols
Each rule reads “right-term is … left-term”; translating the negations gives:
Symbol | Stated meaning (right vs left) | Relation (left → right) |
|---|---|---|
% | neither smaller nor greater | left = right |
& | neither greater nor equal | right < left, i.e. left > right |
* | neither smaller nor equal | right > left, i.e. left < right |
$ | not greater than | right ≤ left, i.e. left ≥ right |
α | not smaller than | right ≥ left, i.e. left ≤ right |
Application — decode the statements
U $ L α K % T → U ≥ L, L ≤ K, K = T
W & P → W > P
D * J → D < J
W % R $ L → W = R, R ≥ L
M * T α J → M < T, T ≤ J
Testing each conclusion
M < W: We have M < T = K and W = R ≥ L with L ≤ K. So M and W meet only around K/L, but the path is M < K, L ≤ K and W ≥ L — it gives no inequality linking M and W in a single direction. M can be made larger than W (e.g. M just below K while W sits down near L), so M < W is not forced. Not definitely true.
D > K: D enters only through D < J, and K satisfies K = T ≤ J, so both D and K lie below J but the chain to J runs the same way for both — it never forces D above K. D can be placed below K with all statements holding, so D > K is not forced. Not definitely true.
J ≥ P: Here P < W = R ≥ L ≤ K = T ≤ J, while J ≥ T. The link from P up to J passes through W and the “≥/≤” bounds at L, which do not transmit a strict order, so P may end up above J. Hence J ≥ P is not forced. Not definitely true.
Cross-check
For each conclusion a single consistent arrangement makes it fail while every statement still holds: M above W (taking M near K and W near L), D below K (D bound only by D < J), and P above J (P bound only by P < W, with W free relative to J). Since each conclusion is breakable by some valid arrangement, none must hold.
Result
As no conclusion is forced in every valid arrangement, the correct response is “None is true”.