Data Sufficiency

1Judge sufficiency — do not grind the answer

A data-sufficiency item gives a question and two labelled statements. Your job is to decide whether a unique answer is obtainable, not to compute that answer and circle it. The moment a statement pins the question to one value (or to a definite yes or no), the statement is sufficient — stop.

Candidates who finish the arithmetic lose time and often mis-map the five options, because they were solving a different exam from the one printed. The skill is knowing when to put the pen down.

Cover the algebra after the line that yields a unique x. The remaining steps are optional decoration; sufficiency was already decided on that first unique value.

How it works

1. Read the question firstUnderline exactly what is asked — a value, a yes/no, or a comparison — before opening either statement.
2. Ask uniqueness, not magnitudeAs soon as one statement forces a single answer to that question, mark it sufficient and move on.
3. Refuse the extra algebraDo not simplify further, pick an option letter, or chase a second confirmation once uniqueness is settled.

2Test each statement alone — never leak

Evaluate statement (1) with statement (2) completely covered, then reverse. Never carry a fact from one statement into the other's individual test. Information leaked across that boundary is the single most common way a C becomes an accidental A or B on paper.

Only after both alone-tests fail do you uncover both statements and ask whether the combination fixes a unique answer. The order is mechanical: (1) alone, (2) alone, then both.

Figure. Two sealed boxes with a hard divider: each alone-test stays inside its own box until both have failed.

How it works

1. Cover (2)Judge statement (1) as if statement (2) did not exist on the page.
2. Cover (1)Judge statement (2) the same way — no leftover numbers from the first pass.
3. Combine lastOpen both only when each alone-test returned insufficient.

3Sufficient means exactly one answer

A statement is sufficient only if it yields exactly one possible value or answer to the question asked. If two different values remain possible, the statement is insufficient — even when both values look plausible and both satisfy the statement.

Squared equations are the classic trap: x^2 = 16 looks like it names x, but it names two roots. Relevance is not uniqueness. Always try to invent a second valid value before calling a statement sufficient.

Figure. Number line with both roots of x^2 = 16: two answers means statement (1) cannot decide x > 0.

How it works

1. List the candidatesFrom the statement alone, write every value (or yes/no outcome) still allowed.
2. Count themOne candidate → sufficient. Two or more → insufficient.
3. Hunt a second rootFor even powers, absolute values and digit-sum conditions, deliberately search for a second valid case before stopping.

4The fixed five-option ladder

CAT-style data sufficiency uses the same five choices every time: (A) statement (1) alone sufficient but (2) not; (B) statement (2) alone sufficient but (1) not; (C) both together sufficient but neither alone; (D) each alone sufficient; (E) even both together insufficient. Memorise the ladder cold — every item maps onto it.

The test order that fills the ladder without double work is (1) alone, then (2) alone, then both. Landing on D means each alone-test already succeeded; landing on E means the combination still leaves two answers open.

Figure. Standard test order: (1) alone, then (2) alone on each branch, then both only when neither alone works. Leaves are A–E.

5Combine only after both alone-tests fail

If neither statement alone suffices, put them together and ask the uniqueness question again. Together they are sufficient when the combination fixes exactly one answer; they are insufficient when two answers still survive — including when the second statement merely restates the first.

Overlapping constraints are the trap behind many E answers: digit-sum 9 and divisible by 9 describe the same two-digit family, so combining adds nothing. Always check whether the second statement introduces a new constraint.

Reuse the fixed five-option ladder from the previous concept: both alone-tests fail, so the path drops to the both? node — here a=10 with a−b=4 fixes a+b=16 (C), not a redraw of that tree beside new algebra.

How it works

1. Confirm both alone failWrite insufficient under (1) and under (2) before you allow yourself to combine.
2. Merge the constraintsSolve the system, or list the values that satisfy both statements at once.
3. Ask uniqueness againOne surviving answer → C. Two or more, or identical restated constraints → E.

6Yes/no stems: a firm no is still an answer

On a yes/no question, a statement is sufficient when it forces a definite yes or a definite no — consistency, not positivity, is the test. A statement that sometimes says yes and sometimes says no is insufficient, even if every case looks tidy.

Do not reject a statement because the answer it forces is no. A locked-in no answers the question asked; only a maybe fails sufficiency.

Figure. On a yes/no stem, sufficiency is a locked outcome. Statement (1) always forces even — a firm yes. Statement (2) still splits (3 odd, 6 even), so it fails even though some cases look tidy.

How it works

1. Name the yes/no questionWrite the exact binary question — Is n even? Is the rectangle a square? — before testing statements.
2. Force one sideAsk whether every value allowed by the statement gives the same yes, or the same no.
3. Reject a splitIf one allowed value says yes and another says no, mark insufficient.