Each of the questions below consists of a question and two statements numbered…
2023
Each of the questions below consists of a question and two statements numbered I and II given below it.
You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements.
How is 'came' written in the code language?
I. 'we came by car' is written as '4 9 2 8' and 'can we buy car' is written as '5 8 0 2'.
II. 'can car be cheap' is written as '8 1 5 3' and 'came by cheap car' is written as '9 8 4 1'
- A.
if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- B.
if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- C.
if the data either in statement I alone or in statement II alone are sufficient to answer the question.
- D.
if the data even in both statements I and II together are not sufficient to answer the question.
Show answer & explanation
Correct answer: D
Concept: In coded-sentence data-sufficiency problems, a word's code can be pinned down only when some statement isolates it - either alone, or paired only with a word whose code is already uniquely known. If two (or more) words always appear together across every sentence given, and no statement ever separates them, their codes stay interchangeable as a SET no matter how many such statements you combine.
Application:
From Statement I: 'we came by car' -> 4 9 2 8, and 'can we buy car' -> 5 8 0 2. The two sentences share the words 'we' and 'car', and the digits common to '4928' and '5802' are 2 and 8. So {we, car} occupy {2, 8} as a set, which leaves {came, by} occupying the remaining {4, 9} as a set - Statement I alone never tells us which of 4 or 9 belongs to 'came'.
From Statement II: 'can car be cheap' -> 8 1 5 3, and 'came by cheap car' -> 9 8 4 1. These share 'car' and 'cheap', and the digits common to '8153' and '9841' are 8 and 1. So {car, cheap} occupy {8, 1} as a set, leaving {came, by} occupying the remaining {9, 4} as a set - Statement II alone has exactly the same gap.
Combining both: 'car' is common to Statement I's {we, car} = {2, 8} and Statement II's {car, cheap} = {8, 1}; the only digit in both sets is 8, so car = 8, which then fixes we = 2 and cheap = 1. But 'came' and 'by' still only appear together, mapped to the same set {4, 9}, in both statements - nothing in either statement, or in the two together, ever places 'came' and 'by' in separate sentences or pairs one of them with an already-known code.
Cross-check: Since 'came' and 'by' never occur apart from each other in any sentence given, no combination of the two statements can break the tie between their codes - confirming the ambiguity survives even after using both statements together.
Hence, the data even in both Statements I and II together are not sufficient to answer the question.