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

Write the solution immediately.

Answer

Skip to the final step.

Answer

Estimate the answer.

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

Multiply x and y and set them equal to the total.

Answer

Subtract the total from x and y.

Answer

Write the equation as x * y = total.

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

Ignore the units of measurement.

Answer

Guess the answer and check if it seems reasonable.

Answer

Use a calculator to double-check the numbers.

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

Convert the percentage to a fraction and divide it by the number.

Answer

Add the percentage to the given number.

Answer

Subtract the percentage from the given number.

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

Add more variables to the equation.

Answer

Multiply both sides by the variable.

Answer

Divide both sides by the coefficient.

Question 6

How do you handle a word problem that involves multiple steps?

Accepted Answer

Work through each step one at a time and keep track of your calculations.

Answer

Guess the final answer and check if it’s reasonable.

Answer

Skip the intermediate steps and go straight to the final answer.

Answer

Multiply all the numbers together.

Question 7

When solving a problem with fractions, what should be the first step?

Accepted Answer

Find a common denominator or simplify the fractions.

Answer

Convert the fractions to decimals.

Answer

Multiply both fractions by the same number.

Answer

Add the fractions directly without simplifying.

Question 8

What is the strategy for solving a word problem involving averages?

Accepted Answer

Add all the numbers together and divide by the total count.

Answer

Multiply all the numbers together and divide by the total count.

Answer

Subtract the smallest number from the largest number.

Answer

Add the numbers in pairs and find the middle value.

Question 9

How do you solve a problem that involves time and distance?

Accepted Answer

Use the formula distance = rate × time.

Answer

Add the rate and time together to find the distance.

Answer

Divide the time by the distance to find the rate.

Answer

Multiply the distance by the rate and divide by the time.