DSAT Problem Solving Strategies 2

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?

Accepted Answer

Distribute 3 on the left side

Answer

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?

Accepted Answer

At the vertex

Answer

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?

Accepted Answer

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

Answer

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?

Accepted Answer

Identify and label the unknown quantity

Answer

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?

Accepted Answer

100 × 1.30 × 0.80

Answer

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

(DSAT) Digital SAT Practice Test