DSAT Problem Solving Strategies 2 — Questions and Answers
Question 1: A student needs to find the value of x in the equation 3(x + 4) = 2x + 17. Which first step is most efficient?
- Divide both sides by 3
- Distribute 3 on the left side (Correct answer)
- Subtract 2x from both sides
- Add 17 to both sides
Correct 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.
Question 2: When a problem asks for the 'minimum' value of a quadratic expression that opens upward, where is that value located?
- At the y-intercept
- At the vertex (Correct answer)
- At the x-intercepts
- At the axis of symmetry's y-value, which equals the vertex
Correct answer: At the vertex
For an upward-opening parabola, the vertex represents the minimum point of the function.
Question 3: 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?
- Set up a proportion: 3/5 = 24/x (Correct answer)
- Multiply 24 by 5
- Subtract 3 from 24, then add 5
- Divide 24 by 5, then multiply by 3
Correct 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.
Question 4: On the DSAT, if a question involves a complex multi-step word problem, what is the best first action?
- Immediately write an equation
- Identify and label the unknown quantity (Correct answer)
- Try all four answer choices
- Convert all units to the same system
Correct 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.
Question 5: 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?
- 100 × 1.30 × 0.80 (Correct answer)
- 100 × (1.30 − 0.20)
- 100 × (0.30 − 0.20)
- 100 × 1.10
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.
Question 6: When working with an SAT problem involving absolute value |x − 3| = 7, how many solutions should you expect?
- Zero solutions
- Exactly one solution
- Two solutions (Correct answer)
- Infinitely many solutions
Correct answer: Two solutions
An absolute value equation of the form |expression| = positive constant always produces two solutions: x − 3 = 7 and x − 3 = −7.
Question 7: A question gives a table of values and asks which linear equation fits. What is the most reliable strategy?
- Pick the equation with the largest slope
- Calculate the slope from two table points and check the y-intercept (Correct answer)
- Plug x = 0 into each answer choice
- Choose the equation whose coefficients look simplest
Correct 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.
DSAT Problem Solving Strategies 2
A student needs to find the value of x in the equation 3(x + 4) = 2x + 17.
Which first step is most efficient?