Lesson Guide
Explanation
Most questions hand you facts and ask for the answer. Sufficiency questions flip it: the outcome is unknown, and you're asked WHICH EXTRA FACT would settle it. Treat each option like a key in a lock: add it to what you already know, and ask 'is exactly one outcome now possible?' If yes, the key fits. If things could still go more than one way, wrong key. You're not finding the answer — you're finding the fact that makes the answer findable. It feels strange for about three questions; then it's a routine.
Your Turn
Mystery: 'Ana is 8 or 9 years old.' Which fact settles it: 'Ana goes to school' or 'Ana turned an even age last birthday'? Check: the even one — it forces 8. Going to school allows both.
Watch Out
An option can be interesting, true and USELESS. Only 'does it collapse the possibilities to one?' counts.
Explanation
A vote question: two votes each for different animals, a pet is bought only if EVERYONE backed one animal, every animal got at least a vote — which extra fact settles the result? Work each option to its end. 'No student voted for both rabbit and lizard': every student's two votes are then rabbit+fish or fish+lizard — both contain fish — so every single student voted for the fish. Unanimous: settled, a fish is bought. Options like 'rabbit was most popular' or 'only two voted lizard' leave both outcomes alive: popular isn't unanimous. Chase each option ALL the way to 'settled' or 'still open'.
Your Turn
Mini version: 3 kids, room repaints only if all vote blue. Fact: 'at least one child voted red.' Settled? Check: YES — one non-blue vote kills unanimity. No repaint.
Watch Out
'Most popular', 'more than half' — these feel decisive but rarely settle unanimity questions. Only all-or-one-exception facts do.
Explanation
The stem's known facts are half the machine. In the vote question, 'every colour received at least one vote' looked like scenery — but it's exactly what made the winning option decisive: it guaranteed a red voter whose ballot broke every unanimity. Sufficiency options are never judged ALONE; they're judged COMBINED with everything the stem gave you. So before testing options, list what you already know in short bullets. An option that looks feeble by itself often clicks against a stem fact like a key against its last pin.
Your Turn
Stem: 'Ben's number is between 1 and 10, and it is even.' Option: 'It is bigger than 7.' Settled? Check: even + >7 + ≤10 → only 8 or 10… NOT settled! Two outcomes left. The option fails.
Watch Out
Down to two possibilities is NOT settled. Sufficiency demands exactly one survivor.
Explanation
Wrong options come in three flavours. ALREADY KNOWN: repeats or rephrases a stem fact — adds nothing. INTERESTING BUT IDLE: a colourful true-sounding fact that doesn't touch the possibilities. NARROWS BUT NOT TO ONE: genuinely rules things out, but leaves two outcomes breathing — the cruellest trap, because it feels like progress. The final test never changes: after adding the option, could you WRITE DOWN the outcome with certainty? If you'd still be guessing between two stories, keep looking.
Your Turn
Stem: 'the winner wore a cap.' Options: 'Jai owns a cap' vs 'Jai was the only runner wearing a cap.' Which settles who won? Check: the ONLY one — owning a cap narrows nothing (others may own caps too).
Watch Out
'Only', 'every', 'none' are the settling words. Options without a totality word rarely close the case.
Explanation
The settle-it routine: (1) list the stem facts as short bullets; (2) name the possible outcomes explicitly; (3) add ONE option at a time and chase it to the very end — no half-checking; (4) demand exactly one surviving outcome. Sufficiency questions are the slowest in the paper, so bank time on quicker questions and spend it here without guilt. And remember the settling words — only, every, none. An option carrying one of those is worth testing first. Quiz and exercises!
Your Turn
Stem: 'the class pet is a rabbit or a guinea pig.' Which settles it: 'the pet has long ears' or 'the pet is not a rabbit'? Check: 'not a rabbit' — direct elimination to one. Long ears is suggestive, not certain.
Watch Out
Never pick the option that merely makes one outcome LIKELY. Sufficiency wants certainty, and likely is the bait.
📌 Key Points — this lesson in a nutshell
- Sufficiency questions ask which extra fact SETTLES the outcome — you find the key, not the answer.
- Test options like keys: stem facts + option → is exactly ONE outcome possible?
- Options are judged COMBINED with the stem — list the stem facts first; they do half the work.
- Down to two possibilities is NOT settled. Demand one survivor.
- Wrong options: already known, interesting-but-idle, or narrows-but-not-to-one.
- Settling words are 'only', 'every', 'none' — options without a totality word rarely close the case.
Step 1: Introduction
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