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Ranking by Elimination
Extremes First
Summary
Start with the two you can actually see
Four angles give you six possible comparisons, and they are not equally hard. One of them is always the easiest in the item: smallest against largest.
That is structural, not luck. Line the four angles up in their true order and the steps between neighbors are the gaps. The smallest and the largest sit at opposite ends of the whole run, so they are separated by every gap in the set added together. Any other pair spans only one or two of those gaps. Whatever the item, the extremes are further apart than anything else in it.
Panels 1 and 4 are far enough apart to call without hesitation. Panels 2 and 3 are separated by a single gap and take real work. So take the free judgment first — and take it before the hard one, because a shaky reading of the middle pair has a way of contaminating a firm reading of everything else.
Two verdicts, then strike
Decide two things and only two: which panel holds the smallest angle, and which holds the largest. Then go to the choices and strike out
- every ordering that does not open with your smallest, and
- every ordering that does not end with your largest.
Those two claims sit at the two ends of every choice, so they are the fastest thing to check — you read the first and last label and move on.
Rank the four angles from SMALL to LARGE.
Read the extremes here before scrolling. Panel 2 carries the most closed opening in the set and panel 4 the most open one.
In degrees: #2 = 70°, #3 = 86°, #1 = 97°, #4 = 111°. Ray length is a distraction — compare the openings near each vertex.
With smallest = 2 and largest = 4, the strike-out runs like this. Choice A opens with 2 correctly but ends with 1, so it is dead. Choice B ends with 4 correctly but opens with 3, so it is dead. Choice D also ends with 4, but opens with 1 — dead. Choice C is the only ordering that both opens with 2 and ends with 4, and the item is over. Panels 3 and 1, the two middle angles, were never compared to each other at all.
How much that usually buys
Roughly half the time, the extremes pass ends the item exactly like that, with one choice standing. The rest of the time two choices survive it — and in the practice items, two is the ceiling. If three of your four choices survive an extremes check, you have misjudged one of the extremes, and the right move is to look again rather than to press on.
In degrees: #3 = 53°, #4 = 62°, #1 = 71°, #2 = 85°. Ray length is a distraction — compare the openings near each vertex.
This item shows the other outcome, and it also shows why you read the choices as well as the angles. Here the smallest is panel 3 and the largest is panel 2 — but every choice already opens with 3, so the "smallest first" test eliminates nothing. All the work is done by the other end: B ends with 1 and C ends with 4, so both die, while A and D both end with 2 and both survive. The item is not finished, but it has shrunk from four choices to two, and the two that remain disagree about one thing only. Settling that is the next topic.
Commit before you look at the middle
Do the extremes pass as a closed operation: judge, strike, and only then move on. The temptation is to hold everything open — to keep all four panels in play while you form a general impression — and it costs you the one advantage the extremes give you, which is that their verdict is trustworthy.
The middle comparison is the least reliable judgment in the item. If you make it while your extremes are still provisional, an error there can talk you out of a reading you had every right to trust. Bank the certain thing first.
When the extremes will not separate
Sometimes you look at all four and cannot confidently say which is smallest, or which is largest. That is not a signal to try harder. The extremes are the widest-separated pair in the item; if that comparison will not come, then every remaining comparison in that item is narrower still, and grinding on it buys nothing but time you will want later.
Flag it, answer it, and move. An item whose extremes are unreadable is an item to spend twenty seconds on, not ninety.
The takeaway
Judge the smallest and the largest first — they are separated by every gap in the set, which makes theirs the easiest comparison the item contains and the most powerful one to eliminate on. Strike every ordering that does not open with your smallest or end with your largest. About half the time that finishes the item outright, and it never leaves more than two choices standing; if it seems to leave three, re-read the extremes. If they will not separate at all, flag the item rather than grinding it.
Practice Questions
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