What Is Data Sufficiency in Reasoning and Quant?
A data sufficiency (DS) question gives a question and two (sometimes three) statements. You do not find the answer itself: you decide which statements are enough to find exactly one answer. SBI PO, IBPS PO, RRB PO and the Clerk mains papers ask DS in both reasoning (blood relations, direction, ranking, seating, coding) and quantitative aptitude (ages, trains, equations, numbers).
Key takeaway: Test statement I alone, then statement II alone, and only then both together. "Sufficient" means it gives one definite answer, including a definite "No". Never carry information from statement I into your check of statement II.
Every answer below was checked in Python: equations solved with sympy and every reasoning case brute-forced over all possible arrangements.
Data Sufficiency Answer Options (Bank Exam Format)
| Option | Meaning |
|---|---|
| (a) | Statement I alone is sufficient, but II alone is not |
| (b) | Statement II alone is sufficient, but I alone is not |
| (c) | Either I alone or II alone is sufficient |
| (d) | Neither I nor II, even together, is sufficient |
| (e) | Both I and II together are needed; neither alone is enough |
Some papers swap the letters of (d) and (e). Read the directions once at the start of the set and write the mapping in the margin.
How to Solve Data Sufficiency Questions (3-Step Method)
- Read the question and decide what "one answer" looks like (a single name, a single number, or a firm Yes/No).
- Statement I alone. Cover statement II with your hand. If one answer comes out, options (a) or (c) are still alive; if not, (b), (d) or (e).
- Statement II alone, then both together only if neither alone worked.
Time saver: in quant DS you rarely need to solve. If you have two independent linear equations in two unknowns, they are sufficient; stop there.
Data Sufficiency Questions with Answers (SBI and IBPS PO Pattern)
1. Ranking. Is P taller than Q? I. P is taller than R. II. R is taller than Q. Alone, neither links P with Q. Together: P > R > Q, so Yes. Answer (e).
2. Linear equations. What is the value of x? I. 2x + 3y = 12. II. x − y = 1. Each has infinitely many solutions alone. Together: x = 3, y = 2. Answer (e).
3. Coding. In a certain code, what is the code for "eats"? I. "pit na sol" means "he eats mango" and "sol ri ka" means "mango is sweet". II. "na lu" means "eats fast". From I, "sol" = mango, so "eats" is "pit" or "na" (two answers). II alone gives "na" or "lu". Together, the common code is na. Answer (e).
4. Direction sense. In which direction is point Q from point P? I. P is 5 m north of R. II. Q is 5 m east of R. I has no Q; II has no P. Together, Q is 5 m east and 5 m south of P: south-east. Answer (e).
5. Number divisibility. Is the positive integer n divisible by 6? I. n is divisible by 3. II. n is divisible by 4. I alone: 3 (No) and 6 (Yes). II alone: 4 (No) and 12 (Yes). Together n is a multiple of 12, so Yes. Answer (e).
6. Trains (either type). What is the length of the train? I. Running at 54 km/h it crosses a pole in 12 seconds. II. Running at 54 km/h it crosses a 120 m platform in 20 seconds. 54 km/h = 15 m/s. I: 15 × 12 = 180 m. II: 15 × 20 − 120 = 180 m. Each alone gives one answer. Answer (c).
7. Inequality trap. Is x > y? I. x² > y². II. x > 0. I alone: x = 3, y = 2 gives Yes, x = −3, y = 2 gives No. II alone says nothing about y. Together: x is positive and |x| > |y|, so x > |y| ≥ y: Yes. Answer (e).
8. Linear seating. A, B, C, D and E sit in a row facing north. Who sits in the middle? I. A sits at an extreme end and C sits second to the right of A. II. D sits at the right end and B does not sit next to D. I: C is second to the right of A, so A must be at the left end and C in the middle. I alone gives C. II alone allows A, B, C or E in the middle. Answer (a).
Data Sufficiency Tricks for Bank Exams
| Situation | Quick rule |
|---|---|
| Two independent linear equations, two unknowns | Sufficient together |
| One equation, two unknowns | Not sufficient alone (unless only a ratio or sum is asked) |
| Ratio given, actual value asked | Need one actual quantity |
| Yes/No question | A definite "No" is sufficient |
| Squares or even powers in a statement | Check negative values before saying sufficient |
| Seating / ranking | A statement that fixes one person at an end often fixes the rest |
| Blood relation | Gender of the asked person must be known |
Common Mistakes in Data Sufficiency
- Solving fully when you only need to know a solution exists.
- Mixing statements: using a fact from I while checking II alone.
- Treating "No" as "not sufficient".
- Ignoring negative numbers and zero in number DS.
- Assuming a gender from a name in blood-relation DS: names alone do not fix gender.
Data Sufficiency Practice Questions
- What is R's present age? I. R is 4 years older than S. II. The sum of the ages of R and S is 30. Answer (e): together R = 17.
- What is the speed of a boat in still water? I. Downstream speed is 18 km/h. II. Upstream speed is 12 km/h. Answer (e): (18 + 12) ÷ 2 = 15 km/h.
- How is M related to N? I. M is the father of K. II. K is the sister of N. Answer (e): M is N's father.
- Is the integer k odd? I. 3k is odd. II. k + 2 is odd. Answer (c): each alone fixes k as odd.
- What is the area of a square? I. Its diagonal is 10 cm. II. The ratio of its side to its diagonal is 1 : √2. Answer (a): I gives side 10 ÷ √2, so area = 10² ÷ 2 = 50 cm². II is true for every square, so it fixes nothing.
Data Sufficiency FAQs
What is data sufficiency in reasoning?
It is a question type where you judge whether the given statements are enough to answer a question, instead of finding the answer itself.
How do you solve data sufficiency questions quickly?
Check statement I alone, then II alone, then both. In quant, stop as soon as you know a single value is possible; do not finish the calculation.
Is data sufficiency asked in SBI PO prelims?
It appears mainly in SBI PO and IBPS PO mains (reasoning and quant), and sometimes in prelims quant as one or two questions.
Is a "No" answer sufficient in data sufficiency?
Yes. If a statement shows the answer is definitely No, the statement is sufficient.
What is option (c) in data sufficiency?
Option (c) means either statement alone is enough, each giving the same single answer.
Practice Next
- Mock tests: SBI PO Reasoning Mini Quiz 02, IBPS PO Reasoning Ability Sectional Mock Test 06, SBI PO Arithmetic Word Problems Test 01 and IBPS RRB PO Reasoning Ability Sectional Mock Test 02; for mains-level DS try the SBI PO Mains Data Analysis and Interpretation Sectional Mock Test 01.
- DS-only practice: SBI PO Data Sufficiency Mock Test 01 (ages, numbers, trains, rectangles and interest, every answer checked case by case).
- Related notes: order and ranking questions for bank exams, blood relation questions for SSC CGL, age problems for bank exams, boats and streams tricks for bank exams and input output reasoning for SBI PO, plus quantity comparison questions.
- Browse all study notes.