PiCAT Preparation: General Science, Arithmetic Reasoning, and Word Knowledge

Adaptations

Heritable characteristics and structures—such as specialized bird feet—that evolve through natural selection to enhance an organism's survival and reproduction in its environment.

Pressure (in coal formation)

The primary geological force that compresses and chemically alters peat over extended time periods to form coal.

Employer Retirement Match Calculation

Determining an employer's matching contribution based on salary and contribution rates; an employee contributing $5\%$ of a $\$50{,}000$ salary ($\$2{,}500$) receives a $25\%$ company match equal to $\$625$.

Total Tank Capacity Problem

Calculating combined maximum volume from fractional fills: Tank A ($\frac{2}{3}$ full with $96\,\text{gallons}$) holds $144\,\text{gallons}$ at capacity, and Tank B ($\frac{4}{5}$ full with $96\,\text{gallons}$) holds $120\,\text{gallons}$, yielding a combined capacity of $264\,\text{gallons}$.

Surface Area of an Open Box (Table Top)

The exposed surface area of a rectangular solid excluding the bottom, calculated as the top face plus four side faces: $(5 \times 3) + 2(5 \times 1) + 2(3 \times 1) = 15 + 10 + 6 = 31\,\text{sq ft}$.

Total Surface Area of a Box

The total outer surface area of a closed rectangular prism, calculated using $2(lw + lh + wh)$; for an $8\,\text{in} \times 12\,\text{in} \times 9\,\text{in}$ box, the area equals $2(96 + 72 + 108) = 552\,\text{sq. in.}$.

Scale Drawing Actual Dimension Calculation

Determining actual physical dimensions using scale ratios and proportions: a $36\,\text{cm}$ height at a $1:20$ scale represents $720\,\text{cm}$ ($7.2\,\text{m}$); with a $4:1$ height-to-width ratio, the actual width is $1.8\,\text{m}$.

Split Investment Interest Calculation

Calculating annual yield on segmented capital: investing $40\%$ of a $\$68{,}000$ salary ($\$27{,}200$) split into $60\%$ in corporate bonds at $7\%$ ($\$1{,}142.40$) and $40\%$ in securities at $12\%$ ($\$1{,}305.60$) earns a total of $\$2{,}448$ in interest.

Fractional Duration Calculation

Finding a fraction of a mixed-number unit of time: running for $\frac{3}{4}$ of a $1\frac{5}{6}\,\text{hours}$ exercise session ($\frac{11}{6}\,\text{hours}$) equals $\frac{3}{4} \times \frac{11}{6} = \frac{33}{24} = 1\frac{3}{8}\,\text{hours}$.

Realtor Commission Percentage

The fee paid to an agent expressed as a percentage of the total transaction: receiving $\$31{,}200$ on a $\$480{,}000$ sale represents $\frac{\$31{,}200}{\$480{,}000} \times 100\% = 6.5\%$.

Allowance Expenditure Percentage

The fraction of total accumulated allowance spent over time: earning $\$5$ weekly for $13\,\text{weeks}$ yields $\$65$; retaining $\$13$ means spending $\$52$, which equals $\frac{52}{65} \times 100\% = 80\%$.

Paving Mix Drum Requirement

The total units of mix required to pave a specific surface area: an area measuring $180\,\text{ft} \times 100\,\text{ft} = 18{,}000\,\text{sq ft}$ covered at $120\,\text{sq ft}$ per drum requires $\frac{18{,}000}{120} = 150\,\text{drums}$.

Photocopy Machine Production Time

The duration needed to process multiple document sets: printing $36\,\text{copies}$ of a $324\text{-page}$ document ($11{,}664\,\text{pages}$ total) at $24\,\text{pages per minute}$ takes $486\,\text{minutes}$, or $8\,\text{hours } 6\,\text{minutes}$.

Intermission Percentage of Event

The proportion of total event runtime occupied by a break: a $27\text{-minute}$ intermission during a $3\text{-hour}$ ($180\text{-minute}$) concert accounts for $\frac{27}{180} \times 100\% = 15\%$.

Triangular Area Formula

The area enclosed by a three-sided figure, calculated as $\frac{1}{2} \times \text{base} \times \text{height}$; a triangular piece of art with a base of $12\,\text{ft}$ and height of $8\,\text{ft}$ requires $\frac{1}{2} \times 12 \times 8 = 48\,\text{sq ft}$ of fabric.

Unrelenting

Persistent; continuing without slackening, stopping, or yielding in intensity.

Gullibility

The susceptibility or tendency of being easily duped, tricked, or deceived.

Impersonate

To pretend to be another person, especially by copying their appearance, mannerisms, or actions.

Deliberately

Intentionally; done consciously, purposefully, and with careful thought.

Adrift