Smarty Buddy CoGAT Practice Test 1: Paper Folding Questions 15 and 16.

Let’s solve each problem step by step.

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Problem 15:

We start with a square piece of paper. The folding steps are shown in the top row:

1. First, the left half is folded over to the right (like closing a book from left to right). So now we have a rectangle that’s half the width.
2. Then, the bottom half is folded up over the top. Now we have a small square — one-quarter the size of the original.
3. On this small folded square, someone draws:
- Two small circles on the left side (which was originally the bottom-left corner area)
- One big square on the right side (which was originally the bottom-right corner area)

Now we unfold it step by step:

→ First, unfold the bottom fold (the vertical fold that brought bottom up to top).
When you unfold vertically, whatever was drawn on the bottom half gets mirrored to the top half.
So the two small circles and the big square will appear both on the bottom AND top halves — but only on the right half of the full paper? Wait — let’s think carefully.

Actually, after first fold (left to right), the paper is halved horizontally. Then second fold (bottom to top) makes it quartered.

The drawing happens on the final folded state — which represents the bottom-right quadrant of the original paper.

When we unfold the second fold (vertical unfold), the bottom-right quadrant mirrors to the top-right quadrant. So now the right half of the paper has:
- Top-right: same as bottom-right → so two small circles and one big square
- Bottom-right: original drawing → two small circles and one big square

Then we unfold the first fold (horizontal unfold — unfolding left to right). That means the entire right half (which now has the pattern) gets mirrored to the left half.

BUT — here’s the key: when you fold left-to-right first, the left half goes UNDER the right half. So when you draw on the folded paper, you’re drawing on the layer that was originally the RIGHT half. When you unfold, the LEFT half will be blank unless something was transferred — but in paper folding puzzles like this, drawings only appear where they were made or mirrored through folds.

Wait — actually, standard rule: when you fold and then draw, upon unfolding, the drawing appears symmetrically across the fold lines.

Let me re-trace:

Original paper: divided into 4 quadrants by dotted lines.

Fold 1: Left half folds over right half → so now visible part is right half, but it’s double-layered (left layer underneath).

Fold 2: Bottom half folds up over top half → now visible is top-right quadrant, but it’s 4 layers thick.

Drawing is done on this top-right quadrant surface.

When we unfold Fold 2 (unfold downward), the drawing appears also in the bottom-right quadrant (mirrored vertically).

Then unfold Fold 1 (unfold leftward), the drawing appears also in the left half — mirrored horizontally.

So overall, the drawing should appear in all four quadrants? But wait — no, because the drawing was only on the outermost layer during folding.

Actually, in these problems, the convention is: whatever is drawn on the folded paper will appear in every position that maps to that spot when unfolded — meaning symmetry across each fold line.

So if you fold left-to-right, then bottom-to-top, and draw on the resulting small square, then when unfolded, the design will be reflected across both the vertical and horizontal center lines.

In this case, the drawing on the folded paper is:

On the small square (which is top-right quadrant of original):

- Left side of small square: two small circles stacked vertically
- Right side of small square: one big square

But note: in the folded state, “left” and “right” correspond to directions within the folded paper.

After unfolding:

First, unfold the vertical fold (bottom to top): so the bottom-right quadrant gets the same as top-right.

Then unfold the horizontal fold (left to right): so the left half gets mirror image of right half.

So let’s map positions:

Final unfolded paper has 4 quadrants:

Top-left | Top-right
Bottom-left | Bottom-right

The drawing was made on what becomes Top-right quadrant.

After unfolding vertical fold: Bottom-right = mirror of Top-right → so same pattern.

After unfolding horizontal fold: Left side = mirror of Right side.

Mirror horizontally means: left and right swap.

So in Top-right: two small circles on left, big square on right.

After horizontal mirror, Top-left will have: big square on left, two small circles on right? No — mirroring flips left-right.

If in Top-right quadrant, the two small circles are on the LEFT side of that quadrant, and big square on RIGHT side...

Then when mirrored to Top-left quadrant, the two small circles will be on the RIGHT side of Top-left quadrant, and big square on LEFT side.

Similarly for bottom row.

But looking at answer choices:

Option A: In top-left quadrant: three small circles on left, big square on right? Not matching.

Wait — perhaps I’m overcomplicating.

Alternative approach: simulate the folds backward.

Start from the last image before answers: the folded paper with drawing.

It shows: on the small square (folded state), there are two small circles on the left, and one big square on the right.

This small square corresponds to the bottom-right quarter of the original paper (since we folded left over right, then bottom over top).

When we unfold the bottom-over-top fold, the bottom-right quarter is revealed, and the drawing is copied to the top-right quarter (because it was folded up).

So now, right half of paper has:

Top-right: two small circles on left, big square on right
Bottom-right: two small circles on left, big square on right

Then we unfold the left-over-right fold. This reveals the left half, and mirrors the right half to the left.

Mirroring horizontally: so for each point on the right, its mirror is on the left.

So in Top-left quadrant: it will be mirror of Top-right.

In Top-right: two small circles on left side of quadrant, big square on right side.

Mirror horizontally: so in Top-left, two small circles will be on the RIGHT side of the quadrant, and big square on LEFT side.

Same for bottom.

So overall:

Top-left: big square on left, two small circles on right
Top-right: two small circles on left, big square on right
Bottom-left: big square on left, two small circles on right
Bottom-right: two small circles on left, big square on right

Now look at answer choices:

A: Has in top-left: three small circles on left, big square on right — doesn’t match.

B: Top-left: two small circles on left, big square on right — but according to us, it should be reversed.

C: Top-left: big square on left, two small circles on right — yes! And top-right: two small circles on left, big square on right — matches.

Bottom-left: big square on left, two small circles on right — matches our prediction.

Bottom-right: two small circles on left, big square on right — matches.

Perfect.

So Problem 15 answer is C.

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Problem 16:

Folding steps:

1. First, left half folds over right half → same as before.
2. Then, instead of folding bottom up, it folds the TOP half down over the bottom half. So now the visible part is the bottom-right quadrant (since left was folded right, then top folded down).

Drawing is done on this folded state: on the small square, there are:

- Left side: three small circles (arranged in triangle? Or just three dots)
- Right side: two big circles (one above other?)

Looking at the drawing in the folded state: it shows on the left part of the small square: three small circles; on the right part: two big circles.

This small square is the bottom-right quadrant of original paper.

Unfolding:

First, unfold the top-down fold (so unfold upward). That means the top-right quadrant gets the mirror image of the bottom-right quadrant.

Since we folded top down over bottom, unfolding will copy the drawing to the top-right quadrant.

So now right half has:

Bottom-right: three small circles on left, two big circles on right
Top-right: same — three small circles on left, two big circles on right

Then unfold the left-over-right fold: mirror the entire right half to the left half.

So left half will be horizontal mirror of right half.

In right half, for each quadrant:

In Bottom-right: three small circles on left side of quadrant, two big circles on right side.

Mirror horizontally: so in Bottom-left: three small circles on RIGHT side of quadrant, two big circles on LEFT side.

Similarly for Top-left: mirror of Top-right → three small circles on right, two big circles on left.

Now check answer choices:

A: Shows in top-left: three small circles on left, two big circles on right — but we need them swapped.

B: Only has two rows? Looks incomplete.

C: Let's see:

Top-left: two big circles on left, three small circles on right — yes! Matches our mirror.

Top-right: three small circles on left, two big circles on right — matches original.

Bottom-left: two big circles on left, three small circles on right — matches mirror.

Bottom-right: three small circles on left, two big circles on right — matches.

Perfect.

So Problem 16 answer is C.

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Final Answer:
15: C
16: C