Problem Solving Strategies Flashcards

A student needs to find the value of x in the equation 3(x + 4) = 2x + 17. Which first step is most efficient?

Answer: Distribute 3 on the left side

Distributing first eliminates the parentheses and simplifies the equation to 3x + 12 = 2x + 17, making it easy to isolate x.

When a problem asks for the 'minimum' value of a quadratic expression that opens upward, where is that value located?

Answer: At the vertex

For an upward-opening parabola, the vertex represents the minimum point of the function.

A ratio problem states that for every 3 apples there are 5 oranges. If there are 24 apples, what strategy finds the number of oranges fastest?

Answer: Set up a proportion: 3/5 = 24/x

Setting up the proportion 3/5 = 24/x and cross-multiplying gives x = 40 oranges directly.

On the DSAT, if a question involves a complex multi-step word problem, what is the best first action?

Answer: Identify and label the unknown quantity

Identifying and labeling the unknown gives you a clear target and prevents misinterpreting what the problem is asking for.

A store marks up items by 30%, then applies a 20% discount. A student wants to find the final price of a $100 item. Which approach is correct?

Answer: 100 × 1.30 × 0.80

Apply each percent change sequentially: 100 × 1.30 gives the marked-up price, then × 0.80 applies the 20% discount, yielding $104.

When working with an SAT problem involving absolute value |x − 3| = 7, how many solutions should you expect?

Answer: Two solutions

An absolute value equation of the form |expression| = positive constant always produces two solutions: x − 3 = 7 and x − 3 = −7.

A question gives a table of values and asks which linear equation fits. What is the most reliable strategy?

Answer: Calculate the slope from two table points and check the y-intercept

Computing slope = (y₂ − y₁)/(x₂ − x₁) from two data points and verifying the y-intercept against the table confirms the correct linear equation.