Data Sufficiency
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Sufficiency Rule | A statement is sufficient if it gives a unique, definite answer. |
| 2 | Options Pattern | (A) Stmt-1 alone, (B) Stmt-2 alone, (C) Both needed, (D) Neither enough – always same order. |
| 3 | Redundant Info | If one statement repeats part of the other, it adds zero new info. |
| 4 | Min-Max Trap | When ranges overlap, check extreme values to see if the answer is still unique. |
| 5 | Hidden Equation | Two linear equations in same two variables → unique solution (sufficient). |
| 6 | Ratio vs Value | A ratio alone never gives absolute value; combine with any absolute datum. |
| 7 | Even-Odd & Divisibility | One odd/even clue often fixes parity; divisibility by 4/8 needs last 2/3 digits. |
10 Practice MCQs
1. How many marbles does Aman have?
I. Aman has 4 marbles more than Bhanu.
II. Bhanu has 6 marbles less than Chitra who has 10 marbles.
Answer: CSolution: From II, Bhanu = 10 – 6 = 4. From I, Aman = 4 + 4 = 8. Both statements required.
Shortcut: Work backwards from the fixed number (10).
Concept tag: Linear equations, fixed reference
2. Is x² – 5x + 6 = 0 ?
I. x is a positive integer < 4.
II. x is prime.
Answer: CSolution: I gives x = 1,2,3. II restricts to primes → x = 2 or 3. Only these satisfy the equation → unique “Yes”.
Shortcut: Plug 2 & 3 directly; both satisfy → sufficient together.
Concept tag: Quadratic root, prime filter
3. What is the speed of the train?
I. Train crosses a 100 m platform in 10 s.
II. Train crosses a pole in 6 s.
Answer: CSolution: Let L = length, S = speed. II gives L = 6S. I gives (L + 100)/S = 10 → 6S + 100 = 10S → S = 25 m/s. Both needed.
Shortcut: Two equations, two unknowns → C.
Concept tag: Train crossing, relative distance
4. In which year was Ravi born?
I. His brother, 4 years older, was born in 1996.
II. Ravi joined school at age 5 in 2005.
Answer: DSolution: I → 2000; II → 2000. Either statement alone gives 2000 → answer is A or B, but since each alone is enough, pick the first that appears sufficient; however, choice set forces “Either I or II” which maps to option “D” in RRB pattern (old NCERT style).
Shortcut: Once you get same year from both, mark “Either statement alone”.
Concept tag: Age translation
5. Is the integer n divisible by 12?
I. n is divisible by 3.
II. n is divisible by 4.
Answer: CSolution: LCM(3,4)=12 → need both.
Shortcut: Recall 12 = 3×4 and 3,4 coprime.
Concept tag: Divisibility rule, LCM
6. What is the area of the rectangle?
I. Perimeter = 30 cm.
II. Length is 2 cm more than breadth.
Answer: CSolution: 2(l+b)=30 and l=b+2 → solve to get l=8, b=6 → area=48. Both required.
Shortcut: Two unique equations → C.
Concept tag: Rectangle formulas
7. Who scored highest among A,B,C?
I. A scored 10 more than B.
II. C scored 20 less than A.
Answer: E (Neither sufficient)Solution: Only relative scores; no absolute comparison to decide highest among three.
Shortcut: No fixed base → can’t rank.
Concept tag: Relative data
8. How many days will 6 men finish the work?
I. 9 men finish it in 12 days.
II. Efficiency of every man is same.
Answer: ASolution: I gives total man-days = 108 → 6 men need 108/6 = 18 days. II is redundant (standard assumption).
Shortcut: Total work = constant → man-days invert proportionally.
Concept tag: Work equivalence
9. Is the triangle right-angled?
I. Sides are 7, 24, 25.
II. One angle equals 90°.
Answer: D (Either)Solution: I satisfies Pythagoras; II directly states right angle. Each alone sufficient → pick “D – Either statement”.
Shortcut: 7-24-25 Pythagorean triad.
Concept tag: Pythagoras, angle definition
10. What is the profit percentage?
I. CP = ₹400.
II. SP = ₹500.
Answer: CSolution: Need both to compute % = (500-400)/400×100 = 25%.
Shortcut: % Profit = (SP-CP)/CP → always needs both values.
Concept tag: Profit % formula
5 Previous Year Questions
1. [RRB NTPC 2021] How many students passed in maths?
I. 80% of 150 students passed in maths.
II. 20% of students failed in maths.
Answer: ASolution: I directly gives 0.8×150 = 120. II gives same 80% passed but needs total; since I already gives total, alone sufficient → A.
Shortcut: % with absolute total → direct calc.
Concept tag: Percentage base
2. [RRB Group-D 2019] Is integer p even?
I. 3p + 2 is even.
II. p² + p is even.
Answer: D (Either)Solution: I → 3p even → p even. II → p(p+1) even always; but for p odd, p+1 even → still even; however, only even p makes statement II trivially consistent, yet reverse is also true. Actually, II is always true for any integer p, so it doesn’t constrain p; hence only I is useful → correction: Answer should be A. (Explanatory correction: II is always even, so no info → only I suffices → mark A).
Shortcut: Parity chain 3p+2 even ⇒ p even.
Concept tag: Parity logic
3. [RRB JE 2018] What is the ratio of ages of A & B?
I. A is 6 years older than B.
II. After 6 years, A will be twice as old as B.
Answer: CSolution: I: A=B+6. II: A+6=2(B+6). Solve → B=6, A=12 → ratio 2:1. Both needed.
Shortcut: Two linear equations → C.
Concept tag: Age problems
4. [RRB NTPC 2016] Is x > 0?
I. |x| = x.
II. x³ > 0.
Answer: D (Either)Solution: I → x≥0; but x=0 also satisfies, yet question is “x>0” – not sufficient alone (x could be 0). II → x³>0 ⇒ x>0 → alone sufficient. So only II suffices → choice B. (Note: pattern allows only A/B/C/D; no single II option → hence correct option tag is B).
Shortcut: x³ sign same as x sign.
Concept tag: Inequality, absolute value
5. [RRB ALP 2018] How long is the platform?
I. Train 120 m long crosses it in 15 s at 54 km/h.
II. Train 120 m long crosses a pole in 8 s.
Answer: ASolution: I: speed = 15 m/s; distance = 15×15 = 225 m → platform = 225 – 120 = 105 m. II: gives speed only → not sufficient alone for platform. Hence only I suffices → A.
Shortcut: Convert km/h to m/s (×5/18); distance = speed × time.
Concept tag: Train & platform
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Two linear equations | Immediately mark “Both together” | l+b=15 & l–b=2 → C |
| One statement repeats question | Redundant → ignore for sufficiency | “find x; I. x is unknown” → II alone decide |
| Unique number property (prime 2, 3) | Plug smallest & check uniqueness | “Is p<5 prime?” II: p=2 → only one value → sufficient |
| Percent with base given | Direct calc → mark alone sufficient | “75% of 800” → calc 600 → A |
| Ratio alone | Never gives absolute → never mark A/B | “A:B=2:3” → needs extra absolute → C |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Treating “Maybe” as “Yes” | They forget sufficiency needs unique answer | Always ask: “Does it give one and only one answer?” |
| Ignoring redundancy | Think more info always helps | If stmt repeats, it adds zero → evaluate other stmt |
| Forgetting standard assumptions | e.g., man-work problems assume same efficiency | Note implicit conditions; if stated explicitly, it may become redundant |
| Mixing range & exact | Range overlap → no unique value | Check min-max extremes before marking sufficient |
Quick Revision Flashcards
| Front | Back |
|---|---|
| Sufficiency test rule | Must yield ONE unique answer |
| Options order (RRB) | A-1 alone, B-2 alone, C-both, D-either/NE |
| 3-4-5 triplet | Right-angled triangle |
| LCM of 3 & 4 | 12 → divisibility by 12 needs both |
| Work formula | M₁D₁ = M₂D₂ (constant work) |
| Profit % | (SP – CP)/CP × 100 |
| Parity rule odd ± odd | Even |
| x | |
| Two equations, two variables | Unique solution → C |
| Ratio alone gives | Proportion, not absolute value |
BETA
