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The Checking Method
When Only the Dotted Lines Differ
Summary
Sooner or later an item hands you two options whose solid line-work is identical — same boundary, same interior, stroke for stroke — and the only difference is in the dashes. That item cannot be answered any other way, and it is the one people rush past.
Two options, one drawing
A and C are the same picture in solid ink: the same plain rectangle, the same proportions, no interior solid lines at all. Not similar — identical. Anything you can do with an outline has already been done, and it has separated nothing.
Both also carry the same dashed horizontal, low across the panel. That line is in both, so it decides nothing either. They differ in exactly one line: a dashed vertical that A puts about a fifth of the way in from the left edge, and C puts down the middle.
Every dashed line makes two claims
A line is dashed because material stands between that edge and your eye. So each dashed line asserts two things at once: the object has an edge at this position, and something is in front of it. Both are already printed in the panels you were given, and you test the position first, because position is faster to check than occlusion.
Position transfers along the dimension the asked view shares with a given view. The asked view here is the end view, so its left-to-right axis is depth, and the near face of the object is the panel's left edge. Depth is exactly what the top view lays out for you.
Read the top view inward from its near edge, which is the bottom. The channel cut into the object stops at a floor about a fifth of the depth back. That floor is the only interior depth the top view records anywhere, and it is where A puts its dashed vertical. C's line sits at half the depth, where the top view draws nothing at all — C is claiming a wall the object does not have.
Seen, or hidden?
Now the second claim, the one that makes the line dashed rather than solid. The top view also shows how far the channel reaches across: it stops well short of both ends of the object, so from either end you are looking through solid material before you get to it. Every edge of that channel is buried, and the end view has to draw all of them dashed.
There is no thickness threshold in that rule. An edge with a hair of material in front of it is dashed exactly as firmly as an edge buried under an inch — the question is never how much stands in the way, only whether anything does. That is why deciding solid-or-dashed is a question you answer by looking at the other panels, not by judging how prominent the feature seems.
How often it comes to this
Not often. Across 135 generated items, eight carried a wrong option whose solid line-work the earlier checks cannot separate from the answer's — about one item in seventeen. That is precisely the frequency built to be forgotten: rare enough that skipping the dashes works most of the time, common enough to cost you a question.
There is also always something there to read. Across 540 options in those 135 items, not one arrived with an empty dashed channel, and neither did any given panel. If you find yourself looking at an option and seeing nothing dashed, you have stopped looking rather than run out of lines.
Reading the dashed channel
Count before you place. Two options carrying different numbers of dashed lines separate in a single glance, and you have not had to locate anything. Only when the counts match do you go line by line, each one against the panel that records its dimension.
Read the dashes last, because they are the slowest part of a drawing to take in — but last is not the same as optional. An item that survives to this stage has no other way out, and the difference will be small, deliberate, and completely decidable from what is already in front of you.
The takeaway
Two options can share an outline exactly and part company only in their dashes. Every dashed line claims an edge at a position and something standing in front of it, and both halves of that claim are drawn in the two panels you were given: the position in whichever given view records that dimension, the occlusion in the material that view shows in the way. Compare counts, then positions. Dotted lines come last in the order and are never the part you drop.
Practice Questions
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