Identifying Relevant Information - SSAT Middle Level Quantitative

1. What is the best plan when a problem compares two ratios and asks for an unknown?

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

2. Identify the setup: "$3$ notebooks cost $9. At the same rate, what is the cost of $5$ notebooks?"

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

3. What should you do when a problem says "$n$ more than" or "$n$ less than" a number?

   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.

4. What is the best plan when a quantity changes by the same factor each step?

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

5. What is the best plan when a problem involves circumference of a circle with radius $r$?

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

6. What is the best plan when a problem says "p\text{%} of a number"?

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

7. What is the best plan when a problem involves area of a triangle with base $b$ and height $h$?

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

8. Identify the relevant information: "Rectangle has length $8$, width $5$, and diagonal $10$. What is the area?"

   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.

9. What should you do when a problem says "$n$ times" a number or "twice" a number?

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

10. What should you do when a problem says "$n$ divided by a number" or "a number divided by $n$"?

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

11. What is the best plan when a quantity increases by the same amount each step?

    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.

12. Identify the equation: "The sum of a number and $7$ is $19$. What equation matches this statement?"

    $x+7=19$. The equation directly translates the verbal sum relationship into algebraic form for solving the unknown.

13. Identify the relevant information: "A book costs $12 plus $3 shipping; tax is $0. What is the total?"

    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.

14. What is the best plan when a problem asks for a percent increase from $A$ to $B$?

    Use \text{percent change}=\frac{B-A}{A}\times 100\text{%}. This formula quantifies relative change, expressing the difference as a percentage of the original value.

15. Identify the operation: "A tank holds $60$ L and is filled at $5$ L/min; how many minutes to fill?"

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

16. What is the best plan when a problem involves area of a circle with radius $r$?

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

17. What is the best plan when a problem gives a total and a rate and asks for time?

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

18. Identify the equation: "$4$ less than twice a number is $10$. What equation matches this statement?"

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

19. What is the best plan when a problem gives a rate and asks for a total amount?

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

20. What is the best plan when a problem involves perimeter of a rectangle with length $l$ and width $w$?

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

21. Identify the setup: "A shirt is discounted 20\text{%} from $30. What expression finds the sale price?"

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

22. What is the best plan when a problem states a total is split into equal groups?

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

23. What is the best plan when a problem involves area of a rectangle with length $l$ and width $w$?

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

24. What is the first planning step when a word problem asks for a specific quantity?

    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.

25. What should you do first if a problem includes extra numbers not needed to solve?

    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.

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