Read the given information carefully and answer the related questions: In a…
2024
Read the given information carefully and answer the related questions: In a certain code language
‘Play the same game.’ is coded as ‘us ud ut uk’ ‘
Seen in the play.’ is coded as ‘uk ua ud um’
‘The jar is seen.’ is coded as ‘ud ua uh uw’
‘The same game played’ is coded as ‘ut ud ub us’
What will be the possible code for ‘game is played’?
- A.
uh ud ub
- B.
ut us ua
- C.
us uh ub
- D.
ut ub ud
- E.
uh uw uk
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept
In a set-based code language, each sentence is given as an unordered group of codes, so word order is not preserved. A word's code is found by intersection: take the code groups of every sentence that contains the word and keep only the code(s) common to all of them. A code that appears in exactly one sentence must stand for the word unique to that sentence.
Application
Decode by elimination, step by step:
“The” appears in all four sentences; the only code present in all four groups is ud, so the = ud.
Comparing “Seen in the play” (uk ua ud um) with “The jar is seen” (ud ua uh uw): the shared words are the (ud) and seen, and the shared codes are ud and ua, so seen = ua.
“Seen in the play” shares play with sentence 1; removing the (ud), seen (ua) leaves play and in mapping to uk, um. Across both play-sentences (1 and 2) the common code is uk, so play = uk, leaving in = um.
In “The same game played” (ut ud ub us), the only code that occurs in no other sentence is ub, and the only word unique to this sentence is played, so played = ub.
Confirmed code mapping:
Word | Code |
|---|---|
the | ud |
seen | ua |
play | uk |
in | um |
played | ub |
game / same | us / ut (interchangeable) |
is / jar | uh / uw (interchangeable) |
game and same always occur together (sentences 1 and 4), so they cannot be separated — each may be us or ut. Likewise is and jar occur together only in sentence 3, so each may be uh or uw. This is exactly why the question asks for a possible code.
Build “game is played”: played = ub (fixed). game ∈ {us, ut} and is ∈ {uh, uw}. So a valid code must be ub together with one of {us, ut} and one of {uh, uw}.
Cross-check
Test each offered code against this requirement:
us uh ub: us (game) + uh (is) + ub (played) — all three are valid choices, so this is a possible code. ✓
uh ud ub: contains ud, which is the, not any of game/is/played.
ut us ua: uses both us and ut (game and same) and ua (seen); it has no code for is and repeats the game/same pair.
ut ub ud: contains ud (the), which does not belong to game/is/played.
uh uw uk: contains uk (play); also pairs uh and uw, which are is and jar, leaving no code for game.
Therefore the possible code for “game is played” is us uh ub.