Data Sufficiency
Data sufficiency asks whether the question can be answered, not what the answer is. You test each statement for exactly one answer and stop the moment you know. Solving to the end wastes time, and solving with both statements at once hides the cases where one alone was enough.
Updated 11 October 2026 · Not in every paper; when it appears, usually a short set under one shared instruction block.
How to think about data sufficiency
Five answer choices, fixed in advance
Every question in a set uses the same five choices: (a) I alone is sufficient, II alone is not; (b) II alone is sufficient, I alone is not; (c) either I alone or II alone is sufficient; (d) I and II together are sufficient, neither alone is; (e) even I and II together are not sufficient. Real papers usually show all five, sometimes in a different order, so read the instruction block once. The practice questions on this page show four of the five, always including the right one.
Sufficient means exactly one answer
A statement is sufficient only if it fixes a single value, or a definite yes or no. If two answers survive — x could be 7 or −7, the person could be a son or a daughter — it is not sufficient, however likely one of them looks. For a yes-or-no question, a definite "no" is just as sufficient as a definite "yes".
Test I alone, then II alone, then together
Cover statement II and judge I on its own. Then cover I and judge II. Combine them only if both fail alone. Keep the two tests separate: a fact from statement I that leaks into your test of II makes II look sufficient when it is not.
Do not solve, count
You never need the actual answer, only whether exactly one exists. For equations, n unknowns need n independent equations, so you can often stop once you have counted them. Check that two equations really are different: 2x + 3y = 26 and 4x + 6y = 52 are the same equation written twice. Use only the data given and general facts (a week has seven days); do not add assumptions the question did not state.
Formulas and shortcuts
- Order of testing
I alone → II alone → I and II togetherCombine the statements only when both fail on their own.
- Exactly one statement works alone
Answer: that statement alone (I alone or II alone) - Each statement works alone
Answer: either statement alone is sufficientNot "both together" — that choice means neither works alone.
- Neither works alone, together they do
Answer: both statements together are needed - Two or more answers survive even together
Answer: even both together are not sufficient - Equations and unknowns
n unknowns need n independent equationsx + y = 10 and 2x + 2y = 20 count as one equation, not two.
- Rank in a row or list
Total = position from one end + position from the other end − 1
Solved examples
Q1. What is Anil's present age? Statement I: Anil is twice as old as Bina. Statement II: Five years ago, Anil was three times as old as Bina.
- Let Anil's age be A and Bina's be B.
- Test I alone: A = 2B. One equation with two unknowns, so A could be 20, 30 or 40. Not sufficient.
- Test II alone: A − 5 = 3(B − 5), which simplifies to A = 3B − 10. Again one equation, two unknowns. Not sufficient.
- Combine: two different equations in two unknowns fix both values. In the exam you can stop here.
- For the record: 2B = 3B − 10 gives B = 10, so A = 20.
Answer: Both statements together are needed (Anil is 20)
Five years ago Anil was 15 and Bina was 5 — three times, as statement II says.
Q2. What is Meena's position from the left end of a row? Statement I: There are 30 students in the row and Meena is 12th from the right end. Statement II: There are 18 students to the left of Meena.
- Test I alone: position from left = total − position from right + 1 = 30 − 12 + 1 = 19. Sufficient.
- Test II alone: 18 students to her left puts her 19th from the left. Sufficient.
- Each statement answers the question by itself, so the choice is "either", not "both together".
Answer: Either statement alone is sufficient (19th from the left)
Both statements give 19, as they must — the statements in a real question never contradict each other. If your two values differ, recheck the arithmetic.
Q3. What is the price of one pen? Statement I: 2 pens and 3 pencils cost Rs 26. Statement II: 4 pens and 6 pencils cost Rs 52.
- Let a pen cost p and a pencil q.
- Test I alone: 2p + 3q = 26 has two unknowns. Not sufficient.
- Test II alone: 4p + 6q = 52, two unknowns again. Not sufficient.
- Combine: divide II by 2 and it becomes 2p + 3q = 26 — the same equation as I. Two statements, one piece of information.
- Both p = 4, q = 6 and p = 7, q = 4 fit, so the price of a pen is not fixed.
Answer: Even both together are not sufficient
Before choosing "both together", check whether one equation is just a multiple of the other.
Practice questions with answers
1. What is the two-digit number? Statement I: The sum of its digits is 9. Statement II: Its tens digit is twice its units digit.
Answer: C. Both statements together are needed — I alone allows 18, 27, 36, 45, 54, 63, 72, 81 and 90. II alone allows 21, 42, 63 and 84. Together, tens = 2 × units and tens + units = 9 give units 3 and tens 6, so the number is 63.
2. What is Kavya's present age? Statement I: Kavya is 6 years younger than her brother. Statement II: Four years ago, Kavya's age was half of what it will be 8 years from now.
Answer: B. Statement II alone is sufficient — I ties Kavya to her brother, whose age is unknown, so it is not sufficient. II has one unknown: K − 4 = (K + 8) ÷ 2, so 2K − 8 = K + 8 and K = 16. II alone is sufficient.
3. How many students are in the class? Statement I: In the class ranking, Rohit is 14th from the top and 23rd from the bottom. Statement II: Sunil is 23rd from the top, 9 places below Rohit.
Answer: A. Statement I alone is sufficient — I gives total = 14 + 23 − 1 = 36. II only places Rohit 14th from the top; nothing fixes the bottom of the list, so the total could be anything from 23 upwards. I alone is sufficient.
4. How is P related to R? Statement I: Q is the mother of P. Statement II: Q is the sister of R.
Answer: D. Even both together are not sufficient — Neither statement alone links P to R. Together, P is the child of R's sister, so P is R's nephew or niece — but P's gender is never given. Two answers survive, so even both statements are not sufficient.
5. Is P greater than R? Statement I: P > Q ≥ R. Statement II: P ≥ S > R.
Answer: B. Either statement alone is sufficient — I gives P > Q ≥ R, so P > R. II gives P ≥ S > R, so P > R again. Each statement answers the question by itself, so either alone is sufficient — not "both together".
6. What is the value of the integer x? Statement I: x² = 49. Statement II: x³ = −343.
Answer: A. Statement II alone is sufficient — I allows x = 7 or x = −7, so it is not sufficient. II allows only x = −7, because the cube of a negative number stays negative. II alone is sufficient.
7. How is T related to V? Statement I: T is the brother of U, and U is the daughter of V. Statement II: V is the mother of T.
Answer: A. Statement I alone is sufficient — In I, T and U are siblings and V is U's parent, so V is T's parent too; "brother" makes T male, so T is V's son. II makes T a child of V but never gives T's gender, so T could be a son or a daughter. I alone is sufficient.
8. Is X greater than Z? Statement I: X > Y. Statement II: Z > Y.
Answer: D. Even both together are not sufficient — Together, X and Z are both greater than Y, but nothing compares X with Z: X = 5, Z = 3, Y = 1 gives yes, while X = 3, Z = 5, Y = 1 gives no. X > Y < Z leads to no conclusion.
Where marks get lost
- Letting a fact from statement I slip into the test of statement II.
- Choosing "both together" when each statement worked on its own — that is "either".
- Counting two equations as two facts when one is a multiple of the other.
- Calling a statement sufficient when two answers survive, such as x = 7 or −7, or son or daughter.
Reading is not practising.
Run a timed set on data sufficiency and see which step you actually lose time on. Free, no card needed.
Start a timed set