Data sufficiency
Data sufficiency questions — free, machine-verified practice
Data sufficiency questions give a question and two statements, and ask which statements are enough to answer it — not what the answer is. Test statement one alone, then statement two alone, and only then both together. The discipline that scores marks is stopping the moment sufficiency is established rather than finishing the arrangement.
Data sufficiency is where strong solvers lose time and weak solvers lose marks, and for opposite reasons. The strong ones solve the puzzle fully and answer correctly after ninety seconds they did not need to spend; the others combine both statements immediately and never discover that one alone was enough. The topic rewards restraint more than skill.
How to answer data sufficiency questions without solving them
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Read the question precisely before either statement
“Who sits at the extreme left?” needs one person named. “What is the seating order?” needs the whole arrangement. Sufficiency is judged against exactly what is asked, so a statement can be sufficient for one phrasing and useless for the other.
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Test statement one with statement two hidden
Cover the second statement physically. The commonest error in the topic is letting a fact from statement two leak into your assessment of statement one, and once the two are mixed they cannot be separated again by memory.
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Ask whether more than one arrangement survives
A statement is sufficient when exactly one answer to the asked question remains. If you can construct two valid arrangements that give different answers, it is insufficient — and constructing that second arrangement is faster proof than reasoning about it abstractly.
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Combine only after both have failed alone
If either statement alone suffices, the combination question never arises. Reach for both together only when each has independently failed, and then ask whether the pair pins the answer down or still leaves two possibilities.
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Stop at sufficiency — do not finish the puzzle
The moment you know one answer survives, you are done. Completing the arrangement earns nothing and costs the minute that the next question needed. This is the single largest time saving available anywhere in the reasoning section.
Choosing the option once each statement is tested
Choosing the option once each statement is tested
| What you found | The answer |
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| Statement I alone works, II does not | I alone is sufficient |
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| Statement II alone works, I does not | II alone is sufficient |
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| Each works on its own | Either alone is sufficient |
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| Neither alone, but both together do | Both together are sufficient |
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| Both together still leave two answers | Even together they are insufficient |
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| Two valid arrangements give different answers | Insufficient — a counter-example settles it |
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Practise data sufficiency questions right now
Every question below was generated by the same engine that mints the Deduce daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.
Question 1
Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
Statement I: Yash lives on a floor somewhere above Nikhil; Arjun lives on a floor somewhere above Uma; There is exactly 1 floor between Uma and Sneha; Yash lives on the floor immediately above Uma.
Statement II: There is exactly 1 floor between Uma and Arjun; Sneha lives on an odd-numbered floor; Uma lives on an odd-numbered floor; There is exactly 1 floor between Yash and Nikhil.
- Statement I alone is sufficient, but II alone is not.
- Statement II alone is sufficient, but I alone is not.
- Each statement ALONE is sufficient.
- Both statements TOGETHER are sufficient, but neither alone.
- Even both statements together are NOT sufficient.
Show the worked solution
- Question: Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
- Statement I (4 clues) alone ⇒ 2 arrangement(s).
- Statement II (4 clues) alone ⇒ 8 arrangement(s).
- Both together ⇒ 1 arrangement(s).
- A statement is "sufficient" exactly when it leaves 1 arrangement. Answer: Both statements TOGETHER are sufficient, but neither alone.
Question 2
Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
Statement I: Manish lives on an odd-numbered floor; Manish lives on a floor somewhere above Aditi; There are exactly 3 floors between Aditi and Geeta; Jaya lives on the floor immediately above Manish.
Statement II: Jaya lives on a floor somewhere above Manish; Gauri lives on an even-numbered floor; Geeta lives on a floor somewhere above Aditi; There are exactly 2 floors between Geeta and Gauri.
- Statement I alone is sufficient, but II alone is not.
- Statement II alone is sufficient, but I alone is not.
- Each statement ALONE is sufficient.
- Both statements TOGETHER are sufficient, but neither alone.
- Even both statements together are NOT sufficient.
Show the worked solution
- Question: Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
- Statement I (4 clues) alone ⇒ 1 arrangement(s).
- Statement II (4 clues) alone ⇒ 3 arrangement(s).
- Both together ⇒ 1 arrangement(s).
- A statement is "sufficient" exactly when it leaves 1 arrangement. Answer: Statement I alone is sufficient, but II alone is not.
Question 3
Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
Statement I: Varun lives on the lowest floor; There is exactly 1 floor between Aditi and Harsh; Aditi lives on an even-numbered floor; Aditi lives on a floor somewhere above Varun; There are exactly 2 floors between Varun and Harsh.
Statement II: Harsh lives on an even-numbered floor; Aditi lives on the floor immediately above Varun; Deepak lives on a floor somewhere above Harsh; Harsh lives on a floor somewhere above Uma; Deepak lives on an odd-numbered floor.
- Statement I alone is sufficient, but II alone is not.
- Statement II alone is sufficient, but I alone is not.
- Each statement ALONE is sufficient.
- Both statements TOGETHER are sufficient, but neither alone.
- Even both statements together are NOT sufficient.
Show the worked solution
- Question: Each person lives on a different floor (1–5). Which statements are sufficient to fix EVERY person's floor?
- Statement I (5 clues) alone ⇒ 2 arrangement(s).
- Statement II (5 clues) alone ⇒ 4 arrangement(s).
- Both together ⇒ 1 arrangement(s).
- A statement is "sufficient" exactly when it leaves 1 arrangement. Answer: Both statements TOGETHER are sufficient, but neither alone.
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Common mistakes
Reading both statements before testing either
Once both are in mind they cannot be un-mixed, and a statement that was insufficient alone will feel sufficient. Cover the second one until the first is judged — physically, not by intention.
Solving the puzzle instead of judging it
Data sufficiency asks whether the answer is determined, not what it is. Every second spent completing an arrangement after sufficiency is established is a second taken from a question that still needed one.
Treating “both together” as the safe default
It is an option, not a fallback. Papers include sets where one statement alone is enough precisely to punish the reflex of combining. Test each alone first, every time.
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FAQ
Do I have to solve the puzzle in a data sufficiency question?
No, and doing so is the main way candidates lose time here. You only need to establish whether the statements pin down a unique answer to the question asked. As soon as you know exactly one answer survives, choose the option and move on — the actual arrangement is worth no marks.
How do I prove a statement is insufficient?
Build two valid arrangements that both satisfy the statement but give different answers to the question. One concrete counter-example settles insufficiency immediately and far faster than reasoning about it in the abstract.
Why do I keep picking “both statements together” wrongly?
Almost always because information from the second statement leaked into your reading of the first. Cover the second statement while judging the first. If either works alone, the combined option is wrong by definition.
Is data sufficiency the same as data interpretation?
No. Data interpretation gives a table or chart and asks you to compute values from it. Data sufficiency gives a question plus two statements and asks only whether they are enough to answer it. They are frequently searched together but test opposite skills — computation versus restraint.
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