PSAT Mathematical Problem Solving

Question 1

What is the first step in solving a word problem?

Accepted Answer

Read the problem and identify the unknowns.

Answer

The first crucial step in solving any word problem is to thoroughly read and understand what is being asked. Identifying the unknowns involves determining what quantities need to be found and what information is provided. This initial comprehension is essential for translating the problem into a solvable mathematical equation or set of steps.

Question 2

Which of the following is the correct way to set up an equation for a problem involving the sum of two numbers?

Accepted Answer

Let x and y represent the numbers, and write the equation as x + y = total.

Answer

The term 'sum' in mathematics specifically refers to the result of adding numbers together. Therefore, to represent the sum of two numbers, 'x' and 'y', equaling a 'total', the correct equation is x + y = total. This directly translates the verbal description into a mathematical expression, forming the foundation for solving the problem.

Question 3

How can you check if your solution to a word problem is correct?

Accepted Answer

Substitute your solution back into the equation or problem and verify the result.

Answer

To verify the correctness of a solution to a word problem, you should substitute your calculated answer back into the original equation or problem statement. If the substituted value satisfies all conditions and makes the equation true, or if it logically fits the context of the problem, then your solution is correct. This step confirms accuracy and catches potential errors.

Question 4

Which of the following strategies is best for solving problems involving percentages?

Accepted Answer

Convert the percentage to a decimal and then multiply it by the given number.

Answer

The most effective strategy for solving problems involving percentages is to first convert the percentage into its decimal equivalent. For example, 25% becomes 0.25. Once in decimal form, you can simply multiply this decimal by the given number to find the corresponding part of the whole, making calculations straightforward and accurate.

Question 5

What is the next step after isolating the variable in a linear equation?

Accepted Answer

Simplify both sides to find the value of the variable.

Answer

After isolating the variable in a linear equation, the next logical step is to simplify the numerical expression on the other side of the equation. This simplification process involves performing any remaining arithmetic operations to calculate the exact numerical value of the isolated variable. This yields the final solution to the equation.

PSAT/NMSQT Practice Test

PSAT/NMSQT Practice Test

PSAT Mathematical Problem Solving