Mentally fold and unfold a paper based on a sequence of folds - CogAT Grades 3 Plus

1. A rectangular piece of paper is folded using a Z-fold pattern (accordion style) creating four equal sections, then rotated 90 degrees and folded in half. A single oval-shaped hole is cut through the center of this configuration. When the paper is returned to its original flat rectangle, how many ovals will be present?
   Answer: 8 ovals arranged in two rows of four ovals each A Z-fold creating four sections means 4 layers, then folding in half after rotation creates 8 total layers (4×2=8). One cut through 8 layers creates 8 ovals. The Z-fold creates 4 positions lengthwise, and the perpendicular fold creates 2 positions widthwise, resulting in 2 rows of 4 ovals each. Choice A ignores the second fold. Choice B miscounts the Z-fold sections. Choice D incorrectly triples one dimension.
2. A circular piece of paper is folded in half three times, creating increasingly smaller semicircular shapes. A small square hole is cut from the curved edge of the final folded shape. When unfolded, what will be the result?
   Answer: 8 square holes arranged in a perfect circle around the center Three folds of a circle in half create 8 layers (2³=8). Since the hole is cut from the curved edge (circumference), when unfolded, the 8 holes will appear evenly spaced around the circle's circumference. Choice B miscounts the folds. Choice C applies incorrect hexagonal symmetry. Choice D incorrectly suggests concentric arrangement.

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