Data Sufficiency: Question: How many doctors are practicing in this town?…
2025
Data Sufficiency:
Question: How many doctors are practicing in this town?
Statements:
(I) There is one doctor per seven hundred residents.
(II) There are 16 wards with each ward having as many doctors as the number of wards.
- 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: B
Concept: A statement in a Data Sufficiency question is sufficient only if it lets you compute one single, unique numerical answer to the question asked, using it together with any general facts already known -- not what that answer turns out to be. If an unknown quantity is needed but never given, the statement is insufficient. Each statement is tested on its own first, before the two are ever combined.
From Statement (I): the given ratio is 1 doctor per 700 residents, so the number of doctors = N / 700, where N is the town's total population. Since N is never stated anywhere in the question, this expression cannot be reduced to one exact number -- Statement I alone is insufficient.
From Statement (II): the number of wards (16) and the number of doctors per ward (equal to the number of wards, i.e. 16) are both given directly. Total doctors = 16 x 16 = 256 -- a single, exact value. Statement II alone is sufficient.
Cross-check: N (the town's population) is not given anywhere else in the question, confirming Statement I genuinely cannot be completed; Statement II's computation uses only the two figures stated in it, with no outside data needed, confirming it genuinely stands alone on its own.
Hence, Statement II alone is sufficient to answer the question, while Statement I alone is not -- so the correct classification is 'II alone is sufficient while I alone is not sufficient'.