Matrix With a Row Rule That Fits Only One Row
On a practice matrix item you have 90 seconds. The 3×3 grid has eight cells shown; the bottom-right is missing. Each cell contains a small polygon and one diagonal slash. Enclosed-region counts by row are: row 1: 2, 3, 4; row 2: 3, 4, 5; row 3: 4, 5, ?. Slash orientation is vertical in every cell of column 1, down-right diagonal in every cell of column 2, and horizontal in every cell of column 3. You initially note that the top row slashes run vertical, down-right, horizontal-a 45° clockwise step-and think the slash rotates along each row. The second row repeats vertical, down-right, horizontal instead of continuing the rotation. The options are: A hexagon with 6 regions and a horizontal slash; B hexagon with 6 regions and a vertical slash; C pentagon with 5 regions and a horizontal slash; D hexagon with 6 regions and a down-right slash. The timer is running.
1. Build the rule table for the two attributes and determine what the missing cell must contain.
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Make a two-attribute table. Regions:
| row | known counts | row rule | missing by row | | 1 | 2,3,4 | +1 | - | | 2 | 3,4,5 | +1 | - | | 3 | 4,5,? | +1 | 6 |
Columns give the same result: column 3 is 4, 5, ? so ? = 6. The two independent directions agree, so the missing cell has 6 regions; this eliminates C.
Slash: columns 1 and 2 each contain three identical orientations (vertical; down-right), and column 3 has two known horizontal slashes. The row-rotation idea is supported only by row 1; row 2 repeats vertical, down-right, horizontal instead of stepping to down-right, horizontal, vertical, so it is not a rule. The missing slash must be horizontal. That leaves A.
2. Why is option D a stronger distractor than option B, and what single check eliminates both?
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Option D uses the correct region count and copies the down-right slash from column 2, which looks like a natural progression from the top row. Option B copies the vertical slash from column 1. Both fail the same test: column 3 is constant horizontal in every known cell, and columns 1 and 2 are constant in all six known cells. A row pattern seen once and contradicted in the second row cannot override a column invariant supported by eight known cells. The check is to ask, for each attribute, whether the proposed rule holds in every complete row or column-not just in the row you first noticed.
3. If only 20 seconds remained, what is the fastest safe order of checks?
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Check regions first: both the row rule and the column rule agree, and one addition removes C immediately. Then check the slash column invariant: column 3 is horizontal in both known cells, which removes B and D in one step. Do not spend time re-testing the row-rotation idea; it already failed on row 2. The final choice is A.