Identifying Relevant Information - SSAT Middle Level: Quantitative

Identify the exact unknown and write it as a variable, such as $x$. Defining the unknown variable establishes a clear foundation for translating the word problem into an algebraic equation.

Ignore the irrelevant numbers and use only values tied to the unknown. Eliminating extraneous data streamlines the problem-solving process by focusing solely on information essential to finding the unknown.

Use division: $ ext{each group}=rac{ ext{total}}{ ext{number of groups}}$. Division evenly distributes the total among the groups, aligning with the equal sharing described in the problem.

Use repeated addition or an arithmetic pattern with a common difference. Arithmetic sequences model linear growth, capturing the constant increment in each step of the quantity's change.

Use multiplication or a geometric pattern with a common ratio. Geometric sequences represent exponential growth or decay, reflecting the consistent multiplication factor applied repeatedly.

Translate to addition or subtraction: $x+n$ or $x-n$. These phrases indicate direct adjustments to the unknown, which translate into basic additive or subtractive operations in algebra.

Translate to multiplication: $nx$ (for “twice,” $2x$). Such phrasing denotes scalar multiplication, directly converting the verbal description into an algebraic expression.

Write $rac{n}{x}$ or $rac{x}{n}$ to match the wording order. The order in division expressions must preserve the problem's wording to accurately represent the relationship between quantities.

Set up a proportion: $rac{a}{b}=rac{c}{x}$ and solve for $x$. Proportions equate ratios, enabling cross-multiplication to solve for the missing value in comparative scenarios.

Convert to a decimal: $p ext{%}=rac{p}{100}$, then multiply by the number. Converting percentages to decimals facilitates multiplication, yielding the portion of the number as required.

Use $ ext{percent change}=rac{B-A}{A} imes 100 ext{%}$. This formula quantifies relative change, expressing the difference as a percentage of the original value.

Use $P=2l+2w$. The perimeter formula sums the sides, efficiently calculating the boundary length for rectangular shapes.

Use $A=lw$. Multiplying length by width gives the enclosed space, standard for rectangular area computation.

Use $A=rac{1}{2}bh$. Halving the base-height product accounts for the triangular shape's area being half that of a parallelogram.

Use $C=2 ext{π}r$. This formula scales the diameter by π to determine the circle's boundary length.

Use $A= ext{π}r^2$. Squaring the radius and multiplying by π computes the circle's enclosed area based on its radial symmetry.

Use $12$ and $3$ only; total is $12+3$. Tax at $0 contributes nothing, so only book cost and shipping are needed to sum the total expense.

Use division: $ ext{time}=rac{60}{5}$. Dividing total volume by fill rate determines the time required, applying the inverse of the rate formula.

Use a proportion: $rac{3}{9}=rac{5}{x}$. The proportion maintains the constant cost per notebook, allowing solution for the unknown cost via cross-multiplication.

Use $30(1-0.20)$. Subtracting the discount percentage from 1 and multiplying by original price yields the reduced amount.

Use $8$ and $5$ only; area is $8\times 5$. Area depends solely on length and width, rendering the diagonal unnecessary despite its presence in the problem.

$2x-4=10$. This setup algebraically captures the operations of doubling and subtracting as described in the statement.

Use $ ext{total}= ext{rate} imes ext{time}$ (or $ imes ext{quantity}$). The formula computes the total by scaling the rate over the given time or quantity, matching rate-based accumulation problems.

Use $ ext{time}=rac{ ext{total}}{ ext{rate}}$. Rearranging the rate formula isolates time, providing a direct method to find duration given total and rate.