Data Sufficiency for RBI Grade B — Statement Analysis and Condition Evaluation

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Concept

Data Sufficiency is not about solving a problem — it is about deciding whether a problem can be solved. That shift in thinking is everything. Most candidates waste 90 seconds actually computing an answer when the question only asks whether enough information exists to compute one.

Here is the core idea: you are given a question and two statements. Your job is to determine which combination of statements provides exactly the information needed to answer the question definitively. Not approximately. Not probably. Definitively — with one and only one answer.

Think of it like a courtroom. The judge doesn't need the full confession to declare guilt — they need sufficient evidence. Statement I is one witness, Statement II is another. Sometimes one witness is enough. Sometimes you need both. Sometimes even both together leave the verdict open.

The analogy that works in the exam hall: imagine you are trying to identify a locked room in a building. Statement I might say "the room is on the third floor." Statement II says "the room has a blue door." Together they might uniquely identify one room — or there might still be three blue-doored rooms on the third floor. Your job is to check whether the combination narrows it to exactly one answer.

For RBI Grade B, Data Sufficiency questions typically appear in the Reasoning section and test your ability to quickly assess algebraic relationships, number properties, geometric conditions, and statistical quantities. The questions are designed to punish two habits: (1) actually solving the full problem when you only need to check solvability, and (2) assuming that partial information means no information.

The standard answer options you will encounter are:

Memorize these five outcome types before the exam. Every question maps to exactly one.


Deep Dive

The Evaluation Protocol

There is a strict order of evaluation you should follow for every single question. Deviating from it causes errors.

Step 1: Read the question stem carefully. Identify exactly what is being asked — a value, a yes/no, a comparison, a ratio.

Step 2: Test Statement I alone. Treat Statement II as if it does not exist. Ask: does Statement I alone give me one definitive answer?

Step 3: Test Statement II alone. Treat Statement I as if it does not exist. Ask: does Statement II alone give me one definitive answer?

Step 4: If neither alone is sufficient, combine both. Ask: do they together give one definitive answer?

Step 5: Map to the five outcome types above.

Never skip steps. Candidates who jump to "both together" skip the check on individual statements and miss questions where one statement alone is sufficient.

Value Questions vs. Yes/No Questions

The standard of "sufficient" differs depending on what the question asks.

Value question ("What is the value of x?"): A statement is sufficient if it produces exactly one numerical value for x. If it gives x = 5 always, it is sufficient. If it gives x = 5 or x = −5, it is not sufficient — you have two possible answers.

Yes/No question ("Is x > 0?"): A statement is sufficient if it always produces the same answer — always Yes, or always No. If under some conditions Statement I gives Yes and under others it gives No, then it is not sufficient. This is where most candidates slip: they find one case where the answer is Yes and stop, not checking whether a No case also exists.

Common Question Categories in RBI Grade B

Category 1: Algebraic Identity

These use factorisation identities. The standard trap is a² - b² = (a+b)(a-b). If you know a² - b² and a - b, you can find a + b by division. Neither piece alone gives you a + b, but together they do. Recognise this structure instantly — it appears frequently.

Category 2: Divisibility Rules

For "Is N divisible by k?", check whether the statement gives you enough to apply divisibility tests. Divisibility by 3: digit sum divisible by 3. Divisibility by 6: must be divisible by both 2 and 3 — so you need two separate conditions, which is why one statement is often not enough.

Category 3: Weighted Averages

Questions like "What is the average salary of group A?" where you know the combined average and average of group B. You need the ratio of group sizes to complete a weighted average calculation: Total average = (n_A × avg_A + n_B × avg_B) / (n_A + n_B). This requires three of the four quantities: combined average, one group's average, and the ratio. If you have only two of these, you cannot solve it.

Category 4: Speed-Distance-Time

The train-platform type. Train crossing a platform: distance = (train length + platform length), time known → gives one equation. Train crossing a stationary man: distance = train length, time known → gives another equation. Two unknowns (speed, train length), two equations — both together sufficient.

Category 5: Geometric Properties

These test whether you know the defining properties of shapes. A rhombus is defined by: (a) all four sides equal, OR (b) diagonals bisect each other perpendicularly. Either of these alone is a complete definition. So each statement alone is sufficient — the answer is Option D.

The Uniqueness Test

Here is the test that separates 90th-percentile scorers from the rest: after you think a statement is sufficient, ask yourself, "Is there any other value / answer that also satisfies this statement?" If yes, the statement is not sufficient.

Example: "Is x a positive number?" with Statement I: x² = 9. This gives x = 3 or x = −3. One positive, one negative. Statement I does not definitively answer the yes/no question — it gives "sometimes yes, sometimes no." Not sufficient.

Combining Statements: The Addition Test

When combining statements, be careful not to add conditions that are not stated. Only use information explicitly given. Do not infer that because Statement I says "x is odd" and Statement II says "x < 10", x must be 1, 3, 5, 7, or 9 — all of these are valid x values, and if the question asks for the value of x, the combination is still not sufficient.


Memory Tricks & Shortcuts

patternISLAND First — Always Test Alone Before Together

Before combining any statements, always test each as an ISLAND. If Statement I alone solves the question, stop — you don't need to check combinations. Most candidates combine first and miss the single-statement answer.

Micro-example: "What is x + y?" with St.I: x + y = 8. Stop. Statement I tells you x + y directly — no need to read Statement II at all. Answer is Option A.

Speed gain: skips two evaluation steps. Standard approach (test both alone, then combined): 3 steps. ISLAND-first (stop at St.I): 1 step when applicable. Saves 30-40 seconds on easy questions.

patternIdentity Spotter — Factor Before You Evaluate

When you see a² - b², a³ - b³, or (a+b)² - (a-b)², factor immediately before deciding sufficiency.

a² - b² = 24(a+b)(a-b) = 24. Now you see: if you know (a-b), you can find (a+b) by division. This instantly tells you that Statement I alone (giving a² - b²) plus Statement II alone (giving a - b) together are sufficient — and neither alone is.

Standard approach (trying numbers): 60 seconds. Factoring first: 10 seconds. The factored form shows exactly what missing variable links the two statements.

patternRule-Count Method for Divisibility

For "divisible by N?" questions, count how many divisibility rules are needed. Divisible by 6 = 2 rules (÷2 and ÷3). Divisible by 12 = 3 rules (÷4 and ÷3). Divisible by 3 = 1 rule (digit sum ÷ 3).

If the question needs 2 rules and each statement covers exactly 1 rule, the answer is almost always Option C (both together, neither alone). If the question needs 1 rule and one statement directly covers it, the answer is Option A or B.

This pre-analysis takes 5 seconds and immediately narrows the answer from 5 options to 2.

eliminationWeighted Average Checklist — 3 Knowns Needed

For any weighted average question: Combined avg = (n₁ × avg₁ + n₂ × avg₂) / (n₁ + n₂). You have 4 unknowns. Combined average is usually given in the question stem. That leaves 3 unknowns.

To solve, you need 2 more pieces: either (avg₁ and ratio n₁:n₂), or (avg₂ and ratio n₁:n₂), or (avg₁ and avg₂ — which then gives ratio). If the two statements together give you exactly 2 of the 3 remaining unknowns, the answer is Option C. If one statement gives you both, the answer is Option A or B.

Eliminates wrong answer in 8 seconds by counting knowns before any calculation.

eliminationYes/No Killer — Find the Counterexample First

For yes/no questions, don't try to prove a statement sufficient — try to break it. Find one case where the answer is Yes and one case where the answer is No under the same statement. If both exist, the statement is not sufficient.

Example: "Is x even?" with Statement I: "x is divisible by 4." Try x = 4 (yes, even). Can you find an x divisible by 4 that is not even? No — all multiples of 4 are even. Statement I is sufficient.

Counterexample search: 10-15 seconds. Forward-proof approach: 45-60 seconds. The counterexample method is faster because one failure proves insufficiency instantly.


Fast-Solving Framework

In the exam hall, follow this 5-step decision tree for every Data Sufficiency question:

Step 1 — Classify the question: Value question (find a number) or Yes/No question (confirm/deny a property)?

Step 2 — Identify the "sufficiency condition": What exactly do you need to know to answer? Write it in your head: "I need the value of x+y" or "I need to confirm digit sum is divisible by 3."

Step 3 — Test Statement I alone (as an island): Does it give one and only one answer to your sufficiency condition? If yes, it is sufficient. Mark it.

Step 4 — Test Statement II alone (as an island): Same check. Mark it.

Step 5 — Map to answer:

Time target: 90 seconds per question. If you are spending more than 60 seconds on any single statement test, you are computing — stop and check whether you only need to assess solvability.


Solved PYQs

Why this question: This is the algebraic identity archetype — a² - b² — that RBI Grade B uses to test whether you factor before evaluating. If you try to solve numerically, you waste time.

Previous Year Questionपिछले वर्ष का प्रश्न
What is the value of (a + b)? Statement I: a² - b² = 24 Statement II: a - b = 4
(a + b) का मान क्या है? कथन I: a² - b² = 24 कथन II: a - b = 4
  1. Statement I alone is sufficient
  2. Statement II alone is sufficient
  3. Both statements together are sufficient
  4. Neither statement is sufficient
  1. केवल कथन I पर्याप्त है
  2. केवल कथन II पर्याप्त है
  3. दोनों कथन मिलकर पर्याप्त हैं
  4. न तो कथन I और न ही कथन II पर्याप्त है
Solutionसमाधान
Statement I: a² - b² = 24 can be written as (a+b)(a-b) = 24. But without knowing (a-b), we can't find (a+b). Statement II: a - b = 4 alone doesn't give (a+b). Together: From (a+b)(4) = 24, we get a+b = 6.
कथन I: a² - b² = 24 को (a+b)(a-b) = 24 लिख सकते हैं। लेकिन (a-b) जाने बिना (a+b) नहीं निकाल सकते। कथन II: a - b = 4 अकेले से (a+b) नहीं मिलता। दोनों मिलकर: (a+b)(4) = 24 से, a+b = 6।

Solving path: Factor Statement I immediately: a² - b² = (a+b)(a-b) = 24. This statement gives the product of (a+b) and (a-b), but not either value individually — multiple pairs satisfy this. Statement II says a - b = 4 but gives nothing about (a+b). Together: substitute (a-b) = 4 into (a+b)(4) = 24, so (a+b) = 6. One unique answer — Option C.


Why this question: The weighted average structure is a recurring trap. Candidates see "average salary" and assume one salary figure is enough. It is not — you need the mixing ratio.

Previous Year Questionपिछले वर्ष का प्रश्न
In a company, the average salary of all employees is Rs. 45,000. What is the average salary of female employees? Statement I: The ratio of male to female employees is 3:2 Statement II: The average salary of male employees is Rs. 50,000
एक कंपनी में सभी कर्मचारियों का औसत वेतन Rs. 45,000 है। महिला कर्मचारियों का औसत वेतन क्या है? कथन I: पुरुष और महिला कर्मचारियों का अनुपात 3:2 है। कथन II: पुरुष कर्मचारियों का औसत वेतन Rs. 50,000 है।
  1. Statement I alone is sufficient
  2. Statement II alone is sufficient
  3. Both statements together are sufficient
  4. Each statement alone is sufficient
  1. केवल कथन I पर्याप्त है
  2. केवल कथन II पर्याप्त है
  3. दोनों कथन मिलाकर पर्याप्त हैं
  4. प्रत्येक कथन अकेले पर्याप्त है
Solutionसमाधान
From Statement I alone, we only know the ratio but not the actual salaries. From Statement II alone, we know male average but need female count. Together: If M:F = 3:2 and total average is 45,000 with male average 50,000, we can find female average using weighted average formula.
कथन I से केवल अनुपात पता है लेकिन वेतन नहीं। कथन II से पुरुष औसत पता है लेकिन महिला संख्या चाहिए। दोनों मिलकर: M:F = 3:2 और कुल औसत 45,000 तथा पुरुष औसत 50,000 से भारित औसत सूत्र द्वारा महिला औसत निकाल सकते हैं।

Solving path: Stem gives combined average = 45,000. Statement I gives ratio M:F = 3:2 but no salary figures — not sufficient. Statement II gives male average = 50,000 but no ratio — not sufficient. Together: use weighted average formula. Let F-average = x. (3 × 50,000 + 2 × x) / 5 = 45,000. Solving: 150,000 + 2x = 225,000, so x = 37,500. Unique answer — Option C.


Why this question: Classic divisibility yes/no question. The key insight is that one rule (digit sum) is all you need — and Statement II (evenness) is a red herring.

Previous Year Questionपिछले वर्ष का प्रश्न
Is the two-digit number xy divisible by 3? Statement I: x + y = 12 Statement II: The number xy is even
क्या दो अंकों की संख्या xy, 3 से विभाज्य है? कथन I: x + y = 12 कथन II: संख्या xy सम (even) है।
  1. Statement I alone is sufficient
  2. Statement II alone is sufficient
  3. Both statements together are sufficient
  4. Neither statement is sufficient
  1. केवल कथन I पर्याप्त है
  2. केवल कथन II पर्याप्त है
  3. दोनों कथन मिलाकर पर्याप्त हैं
  4. न तो कथन I और न ही कथन II पर्याप्त है
Solutionसमाधान
Statement I: A number is divisible by 3 if sum of its digits is divisible by 3. Since x + y = 12 and 12 is divisible by 3, the number xy is divisible by 3. Statement II: Being even doesn't determine divisibility by 3.
कथन I: कोई संख्या 3 से विभाज्य होती है यदि उसके अंकों का योग 3 से विभाज्य हो। चूंकि x + y = 12 और 12, 3 से विभाज्य है, अतः संख्या xy, 3 से विभाज्य है। कथन II: सम होना 3 से विभाज्यता निर्धारित नहीं करता।

Solving path: Divisibility by 3 requires: digit sum divisible by 3. Statement I: x + y = 12, and 12 is divisible by 3 — confirmed, always yes. Statement I alone is sufficient. Statement II says the number is even — this tells you about divisibility by 2, not by 3. Completely irrelevant to the question. Option A.


Why this question: Geometric definition questions test whether you know which properties are definitional (sufficient alone) versus necessary-but-not-sufficient.

Previous Year Questionपिछले वर्ष का प्रश्न
Is the quadrilateral ABCD a rhombus? Statement I: All sides of ABCD are equal. Statement II: Diagonals of ABCD bisect each other at right angles.
क्या चतुर्भुज ABCD एक समचतुर्भुज (Rhombus) है? कथन I: ABCD की सभी भुजाएँ बराबर हैं। कथन II: ABCD के विकर्ण एक-दूसरे को समकोण पर समद्विभाजित करते हैं।
  1. Both statements together are sufficient
  2. Either statement alone is sufficient
  3. Statement I alone is sufficient
  4. Statement II alone is sufficient
  1. दोनों कथन मिलाकर पर्याप्त हैं
  2. कोई भी एक कथन अकेले पर्याप्त है
  3. केवल कथन I पर्याप्त है
  4. केवल कथन II पर्याप्त है
Solutionसमाधान
Statement I: A quadrilateral with all sides equal is a rhombus. Statement II: A quadrilateral with diagonals bisecting each other at right angles is also a rhombus. Either property alone defines a rhombus.
कथन I: सभी भुजाएं समान वाला चतुर्भुज समचतुर्भुज होता है। कथन II: विकर्ण एक-दूसरे को समकोण पर समद्विभाजित करने वाला चतुर्भुज भी समचतुर्भुज होता है। कोई भी गुण अकेले समचतुर्भुज परिभाषित करता है।

Solving path: Statement I: all sides equal → a quadrilateral with all equal sides is a rhombus by definition. Sufficient alone. Statement II: diagonals bisect each other at right angles → this is also a defining property of a rhombus (not a square — a square has this property too, but a square is a special case of a rhombus). Either statement alone is sufficient — Option D.


Why this question: Speed-distance-time with two unknowns. Two equations needed. Each statement gives one equation — together they form a solvable system.

Previous Year Questionपिछले वर्ष का प्रश्न
What is the speed of the train? Statement I: The train crosses a 200m platform in 20 seconds. Statement II: The train crosses a stationary man in 10 seconds.
ट्रेन की गति क्या है? कथन I: ट्रेन 200m लंबे प्लेटफॉर्म को 20 सेकंड में पार करती है। कथन II: ट्रेन एक खड़े हुए आदमी को 10 सेकंड में पार करती है।
  1. Statement II alone is sufficient
  2. Neither statement alone nor both together are sufficient
  3. Statement I alone is sufficient
  4. Both statements together are sufficient
  1. केवल कथन II पर्याप्त है
  2. न तो अकेला कोई कथन और न ही दोनों मिलकर पर्याप्त हैं
  3. केवल कथन I पर्याप्त है
  4. दोनों कथन मिलकर पर्याप्त हैं
Solutionसमाधान
From Statement II, train length = speed × 10. From Statement I, (train length + 200) = speed × 20. Substituting: speed × 10 + 200 = speed × 20, solving gives speed = 20 m/s. Both statements needed.
कथन II से, ट्रेन की लंबाई = गति × 10। कथन I से, (ट्रेन की लंबाई + 200) = गति × 20। प्रतिस्थापन: गति × 10 + 200 = गति × 20, हल करने पर गति = 20 मी/से। दोनों कथन आवश्यक।

Solving path: Let train length = L, speed = v. Statement II (stationary man): L = v × 10 → one equation, two unknowns — not sufficient. Statement I (platform): L + 200 = v × 20 → one equation, two unknowns — not sufficient. Together: substitute L = 10v into second equation: 10v + 200 = 20v, so v = 20 m/s. Unique value — Option C.


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