UA Aptitude Test — Everything On One Page

Levers & Fulcrum

• Arm = distance from the fulcrum. Never from the end of the bar.
• Fulcrum near the load → less force needed. (Answer to nearly every "least effort" question.)
• Fulcrum near your hands → more force needed.
• Mechanical advantage = effort arm ÷ load arm.
• MA of 5 → 1/5 the force, but 5× the travel. Never something for nothing.
• Heavier weight always sits on the shorter arm.

Method: multiply the side you know completely, then divide by the number you have on the other side.

Torque & Wrenches

• Double the handle → half the force. That's the cheater bar.
• Same force, longer wrench = more torque.
• Pull perpendicular to the handle. Any angle wastes force.
• Two hands opposite sides of a valve wheel → torques add.

Gears, Pulleys, Belts

• Small drives big → slower, more torque.
  Big drives small → faster, less torque.
• Meshed gears turn opposite ways. Gears 1 and 3 in a row turn the same way.
• An idler gear changes direction only — never the ratio.
• Belts: both pulleys turn the same way unless the belt is crossed.
• Block and tackle: Effort = Load ÷ number of lines supporting the moving block. Pull that many feet of rope per foot of lift.
• "Where is the most force?" → the point with the fewest supporting lines.

Fluids & Pressure

• Pressure depends on HEIGHT ONLY. Not width, not shape, not gallons. A 1" tube 40 ft tall reads the same at the bottom as a pool 40 ft deep.
• Water seeks its own level — connected vessels equalize regardless of shape or size.
• Lower outlet = more pressure. Deeper column above it.
• Same flow through a smaller pipe = faster water.
• Area goes with the square of diameter. Double the pipe = 4× the area. Triple = 9×.
• Water flows from high pressure to low — not simply downhill.
• Moving water loses pressure to friction over distance.

Basic Electricity

SERIES ONE PATH

• Resistances add. Total is bigger than any single one.
• Current is the same everywhere. Voltage divides up.
• Break it anywhere → everything stops.
• Batteries in series add voltage. 6V + 6V = 12V.

PARALLEL SEPARATE PATHS

• Each branch gets full voltage.
• Total resistance is less than the smallest branch. Two equal resistors → half of one.
• Lose one branch, the others keep running at same brightness.

• Resistance goes up with longer/thinner wire, down with shorter/thicker.
• Think plumbing: voltage = pressure, current = flow, resistance = restriction.

Folding · 2D → 3D

• Squares that touch edge-to-edge are always adjacent on the cube — never opposite. Eliminates choices instantly.
• Squares separated by exactly one square in a straight line end up opposite.
• An L-shaped path (over one, then turn) wraps around — those ends land adjacent.
• Pick one square as the base, fold the rest up around it one at a time. Don't build the whole cube at once.
• Watch tabs and which way arrows/patterns point. Orientation counts, not just which faces touch.

Block Counting

• Count by vertical column, not by visible face. Write each column's height down, front to back, then add.
• Nothing floats. A block on level 3 has two buried underneath it.
• Hidden blocks: you see three faces of the pile — top, left, right. A block is fully hidden only when all three of those directions are covered. Only deep interior blocks qualify.
• If two choices are one apart, you miscounted one column — recount that column, not the whole stack.

Rotations

• Rotation never changes handedness. Flipping does. A mirror image can never be spun into the original — that's the wrong answer they plant every time.
• Count the squares/segments first. Different count = instant elimination.
• Pick one distinctive feature (notch, corner, long arm) and track which side the rest sits on. In a mirror, that reverses.
• Turn the paper. Nothing stops you from rotating the booklet.

Fractions & Decimals

• Add/subtract: common denominator first. Shop fractions are all powers of 2, so it's just the largest denominator. 3/8 + 1/16 → 6/16 + 1/16 = 7/16.
• Multiply: straight across, top×top, bottom×bottom. No common denominator.
• Divide: flip the second one and multiply.
• Always reduce. Unreduced answers are planted distractors.
• Decimal → sixteenths: multiply by 16. .4375 × 16 = 7 → 7/16.
• Fraction → decimal: it's division. By hand.

Ratios, Proportions, Algebra

• "1 to 4" means 5 total parts, not 4. Most common miss on the whole math section.
• Proportions: a/b = c/d → cross-multiply → a×d = b×c.
• Rate problems: reduce to one worker, one hour first, then scale up. Never jump crew size to crew size.
• Solving for x: undo operations in reverse, same move on both sides. Plug the answer back in to check.
• Percent: move the decimal two left, multiply. 25% of 160 → .25 × 160 = 40.
• Scale drawings: 1/4" = 1'-0" means 4 ft per inch. 1/8" scale = 8 ft/in. 1/2" scale = 2 ft/in.
• Word problems: write down what's given and what's asked before touching numbers. Most errors are setup errors, not arithmetic.
• 12 inches per foot. Feet × 12 + loose inches.

Reading — 42 Q in 25 Min

• About 35 seconds per question. Pace is the actual test.
• Read the questions first, then the passage. Cheapest points available.
• Main idea: right answer covers the whole passage. Wrong answers are true details covering only one paragraph.
• Detail: the answer is in the passage. Go find it — don't answer from what you already know.
• Answer choices with "always," "never," "all" are usually wrong.