Mixed Deck — All GCAT Topics Flashcards

In a pattern series, a star's points increase by 1 each step: 4-pointed, 5-pointed, 6-pointed, 7-pointed. The stars also alternate between black and white. What is the 5th figure?

Answer: 8-pointed black star

The 5th figure has 8 points (4+4 steps) and is black (odd positions 1,3,5 are black).

Three cubes are stacked vertically. When viewed from the side, you see a tall rectangle. When viewed from the front, you see three squares. What is the arrangement?

Answer: 3 cubes stacked directly on top of each other

Stacking three cubes directly on top of each other produces a single tall rectangle from the side and three visible squares from the front.

A company's revenue grew 20% in Year 1 and then declined 20% in Year 2. What is the net change in revenue after both years?

Answer: −4% below original

Starting at 100, a 20% increase gives 120, then a 20% decrease gives 96, which is 4% below the original value.

A sequence of figures uses an XOR rule: overlapping regions between two shapes disappear. Figure 3 shows a square overlapping a triangle. Which answer correctly describes the XOR result?

Answer: Square and triangle with their shared area removed

XOR removes the region where both shapes overlap, leaving only the non-overlapping parts of each shape.

A rectangular piece of paper 8×11 inches is rolled into a cylinder along its long edge. What is the approximate circumference of the resulting cylinder?

Answer: 8 inches

Rolling along the long edge means the short edge (8 inches) becomes the circumference of the cylinder.

A rule states: approve requests submitted on weekdays before 3 PM; deny all others. A request arrives on Wednesday at 4:15 PM. What is the correct action?

Answer: Deny it

Wednesday is a weekday but 4:15 PM is after the 3 PM cutoff, so the request must be denied.

In a dataset of 9 values, the mean is 14 and 8 of the values sum to 106. What is the 9th value?

Answer: 20

Total sum = 14 × 9 = 126; 9th value = 126 − 106 = 20.

How many times does the digit '3' appear in the following list: 13, 33, 73, 103, 130, 333?

Answer: 9

Counting each digit: 13(1), 33(2), 73(1), 103(1), 130(1), 333(3) = 9 threes total.

Which material property describes a material's ability to return to its original shape after a deforming force is removed?

Answer: Elasticity

Elasticity is the property by which a material recovers its original shape after deformation forces are removed.

A square piece of paper is folded in half diagonally from the top-right corner to the bottom-left corner. Then, the resulting triangle is folded in half again along its line of symmetry. A small circular hole is punched through the center of this final, smaller triangle. What will the paper look like when fully unfolded?

Answer: A square with two holes along the main diagonal.

The first unfold is along the triangle's line of symmetry. This mirrors the single hole, creating two holes in the larger triangle. The second unfold is along the diagonal of the original square. This mirrors the two holes across that diagonal, but since the holes are located on the fold line itself, they do not duplicate. The result is two holes positioned on the diagonal that was used for the first fold.

Exactly three of the five statements below are true. Statement 3 says 'Statement 1 is false.' If Statement 1 is true, how many of statements 2–5 must be true?

Answer: 2

If Statement 1 is true, then Statement 3 is false; with 3 total true among 5 and statements 1 and 3 accounting for one true and one false, exactly 2 more from statements 2, 4, 5 must be true.

A 3×3 matrix assigns each cell a letter based on (row number + column number), where A=1, B=2, etc. What letter belongs in row 2, column 4?

Answer: F

Row 2 + column 4 = 6, and the 6th letter of the alphabet is F.

A flat cross-shaped net is folded into a cube. If the center square is the bottom face, which square becomes the top face?

Answer: The square directly below the center

When folding a cross-shaped net, the square opposite the bottom (directly below the center in the net) becomes the top face.

You monitor four dials simultaneously. Dials A, B, C start at 0 and increase by 3, 5, and 7 per second respectively. After 4 seconds, which dial shows the highest reading?

Answer: Dial C

After 4 seconds: A=12, B=20, C=28 — Dial C is highest.

A TV is sold for $640 at a loss of 20%. What was the original cost price?

Answer: $800

Cost × 0.80 = $640; cost = $640 ÷ 0.80 = $800.

You hold three rules in mind: (1) Boxes over 10 kg need a label. (2) Fragile items need padding. (3) Labeled items go to dock B. A 12 kg fragile box arrives — which dock does it go to?

Answer: Dock B

At 12 kg it exceeds 10 kg so it gets a label, and labeled items go to Dock B.

How many distinct ways can a standard 2×2 Rubik's cube face be oriented if you can only rotate the entire cube (not individual pieces)?

Answer: 24

A cube has 24 possible orientations (6 faces can be on top × 4 rotations per face).

What number comes next? 1, 2, 4, 7, 11, 16, ___

Answer: 22

Differences increase by 1 each step (+1,+2,+3,+4,+5,+6), so 16 + 6 = 22.

PROLOGUE : EPILOGUE :: PREFACE : ?

Answer: Afterword

A prologue comes before and an epilogue comes after a play, just as a preface comes before and an afterword comes after a book.

A train travels 120 miles in 2 hours, then 90 miles in 1.5 hours. What is the average speed for the entire trip?

Answer: 60 mph

Total distance = 210 miles, total time = 3.5 hours; 210 ÷ 3.5 = 60 mph.