Data Sufficiency

Module 02 — Lesson 0002 · In Depth · 50 min

Data Sufficiency doesn't ask you to solve — it asks: do we have enough to know? A single unique value answers "What is x?", a definitive YES or definitive NO answers "Is x>0?". Learn the AD/BCE elimination flow and the three traps that decide most wrong answers.

1. The Anatomy of a Question

Stem + two statements → choose sufficiency, not the numeric answer.

Part	What it does	Example
Question stem	Poses the target	"What is the value of x?"
Statement I / II	Adds data (use independently first)	"x² = 36"
Five options	Categorizes sufficiency	A–E (see below)

The Standard Options — Memorize the Letters

Option	Meaning
A	(1) alone is sufficient, (2) alone is not
B	(2) alone is sufficient, (1) alone is not
C	Both together are sufficient, neither alone is
D	Each alone is sufficient
E	Together are NOT sufficient (even combined)

Mnemonic: A=1, B=2, C=combined, D=both singly, E=even combined fails. In exams, options are often re-labeled — ignore letter, remember meaning: "1 alone / 2 alone / together / each / neither".

2. Key Concepts by Topic — What Counts as "Enough"?

a) Algebra and Equations

Value question: need n distinct linear equations for n variables. Two variables → two equations (e.g., x+y=5 and x−y=1 → unique x,y).
Quadratics: x²=36 gives two values (+6,−6) → not unique → not sufficient unless a constraint like x>0 eliminates one.
Inequalities: x>5 is a range, not a value — rarely answers "What is x?" but may answer "Is x>10?" (if range is entirely above or below the threshold, it is sufficient for a YES/NO question).

b) Number Systems

Integer vs real: never assume integer unless stated — x²=2 has no integer solution but has real ±√2. Many traps hinge on "x is an integer" being unstated.
Divisibility: rules for 3,5 etc. with remainder theorems — often combine to pinpoint a value only together.

c) Geometry

Unique construction: triangle needs 3 distinct pieces (SSS, SAS, ASA) — two angles without a side is not enough.
Coordinates: perpendicular → slopes product = −1; need both slopes.

d) Arithmetic (Word Problems)

Work & rate: Rate × Time = Work — any two gives the third.
Sets (Venn): Total = A + B − Both + Neither — need 3 of 4 to find the 4th.
SI/CI: need 3 of 4 variables (P,R,T,I) to pin the 4th.

General rule: Count unknowns vs independent equations. "What is x?" needs a unique number; "Is x>0?" needs a forced YES or forced NO — either extreme is sufficient as long as it is forced.

3. Strategic Approach — The AD/BCE Method (Elimination Flowchart)

AD/BCE: test (1) alone to halve the options, then (2) alone, only then combine.

(1) alone? Sufficient → answer is A or D (kill B/C/E). Not sufficient → answer is B/C/E (kill A/D).
(2) alone?
- If you kept A/D: (2) sufficient → D, else → A.
- If you kept B/C/E: (2) sufficient → B, else → go to step 3.
Combine (1)+(2): unique answer → C; multiple cases remain → E.

Time saver: After step 1 you have eliminated 3 options — you are now 50/50 (A vs D or B vs C/E). Many test-takers solve fully instead of eliminating.

4. Common Traps to Avoid

Trap 1: Assuming Integer Values

Question: Is x > 5? Statement: x² = 36
Trap: thinking x=6 → YES → sufficient.
Reality: x could be ±6 — two cases, one YES (6>5) and one NO (−6>5 false) → not sufficient. Only with x>0 does it become sufficient (unique YES).
Rule: quadratics give two roots unless a sign constraint eliminates one.

Trap 2: "Is" vs "What" Questions — Sufficiency Means Different Things

Question type	What counts as sufficient	Example
"What is x?"	Single unique value	x=3 sufficient; x=3 or 4 not
"Is x>0?"	Definitive YES or definitive NO (either forced is sufficient)	x=5 → YES (sufficient); x=−5 → NO (sufficient); x=±5 → maybe → not sufficient

If a statement forces NO, it is just as sufficient as one that forces YES — sufficiency is about certainty, not positivity.

Trap 3: Carrying Information Over

Never carry info from (1) to (2) when testing individually. Analyze each in isolation first. Only at step 3 do you combine. Carrying makes (2) look sufficient when alone it is not — the classic A→C error.

5. Summary — Sufficiency Conditions

Question type	Sufficient when
Value: "What is …?"	Exactly one value remains (unique)
Yes/No: "Is …?"	Always YES or always NO (no split)
Combined C vs E	Use all constraints; if multiple cases survive → E

Five options: A means?

Option D means?

To find two variables x,y uniquely, need?

x²=36 alone answers “What is x?”

“Is x>0?” with x=5 alone → sufficient?

“Is x>0?” with x=−5 alone → sufficient?

Statement (1) sufficient → eliminate?

Both alone fail, together give unique value → answer?

Trap: Never carry info from (1) to (2) when?

Notes

Anatomy :-

Stem ⇒ target ; (1)/(2) ⇒ data ; Options ⇒ A=(1) alone, B=(2) alone, C=together, D=each, E=neither

Key by Topic :-

Algebra ⇒ n vars need n eqns ; quadratic ± → not unique ; inequality = range

Number ⇒ don’t assume integer ; Geometry ⇒ 3 pieces for Δ ; Work ⇒ 2 of 3 vars

AD/BCE :-

(1) sufficient → keep A/D (kill B/C/E) ; not → keep B/C/E

(2) on A/D branch: suff→D else A ; on B/C/E branch: suff→B else combine

Combine: unique→C else E

Traps :-

a) Assume integer × ; b) What (unique) vs Is (YES or NO both sufficient) ; c) Carry (1)→(2) × when testing alone

Primary source: none pinned yet — drop your preferred video/book resource into RESOURCES.md and it will be linked here. Ask me anything that's unclear.

← Prev: Series Next: Assumptions, Conclusions & Courses of Action →

Questions? Ask your agent — you can follow up on any concept, quiz answer, or get extra practice problems tuned to this module.