Data sufficiency: the area — Aptitude Question
Data sufficiency: the area: Question: What is the area of a square? Statement I: Its perimeter is 40 cm. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 90 seconds
Question
Question: What is the area of a square?
Statement I: Its perimeter is 40 cm. Statement II: Its diagonal is 10√2 cm.
Which statements are sufficient?
Options
- I alone only
- II alone only
- Either I or II alone is sufficient
- Both together are needed
Show the answer and the worked solution
Correct answer: C. Either I or II alone is sufficient
Worked solution
- I alone: perimeter 40 → side 10 → area 100. Sufficient.
- II alone: diagonal 10√2 → side 10 → area 100. Also sufficient.
- So either statement alone is sufficient.
Answer: Either I or II alone is sufficient.
The idea
When each statement independently pins the answer down, the correct choice is 'either alone'. Check both separately rather than stopping at the first.
Shortcut. A square has only one free dimension, so any single length — side, perimeter or diagonal — fixes its area. Both statements are lengths, so each works alone.
Common trap. "I alone only" — stopping once perimeter 40 → side 10 → area 100 works, without testing II, whose diagonal 10√2 also gives side 10.