How many visitors saw the exhibition yesterday? Statements: Each entry pass…
2023
How many visitors saw the exhibition yesterday?
Statements:
Each entry pass holder can take up to three persons with him/her.
In all, 243 passes were sold yesterday.
- A.
I alone is sufficient while II alone is not sufficient
- B.
II alone is sufficient while I alone is not sufficient
- C.
Either I or II is sufficient
- D.
Neither I nor II is sufficient
Show answer & explanation
Correct answer: D
Concept: A data-sufficiency statement (or combination of statements) is sufficient only when it pins down ONE exact value. If the given information only bounds the quantity between a minimum and a maximum, it is not sufficient, no matter how tight the bound is.
Applying this to the two statements:
Statement I alone only caps how many guests (0 to 3) each pass holder may bring; it says nothing about how many passes were sold, so no visitor count can even be attempted from it by itself.
Statement II alone gives the total passes sold (243) but not how many guests each holder actually brought, so it cannot yield an exact total by itself either.
Combining both: the visitor count is bounded between 243 (if no holder brings any guest) and 243 x 4 = 972 (if every holder brings all three permitted guests) - a range, not a single number, because how many guests each holder actually brought is never stated.
Cross-check: the phrase 'up to three' is the key signal - it caps the guest count, it does not fix it. Had the statement instead said 'exactly three', the two statements together would fix one exact total and become sufficient. Since that is not the case here, no combination of the two statements determines a single figure.
Therefore, neither statement alone, nor the two together, is sufficient to find the exact number of visitors.