Lesson: Data Sufficiency Challenging - 17t07

Easy Math/Tough Applications: Example 2

A home owner must pick between carpet A, which costs $6.00 per square foot, and carpet B, which costs $4.50 per square foot. If the home owner must pay the installer the same rate regardless of which carpet is used, which of the two carpets will be cheaper to install?

1) Carpet B takes one-third longer to install than carpet A.

2) Labor costs are $20 per hour.

Review the question stem above. What other factor must we take into consideration when determining the total cost of Carpet A and Carpet B? Type your answer into the Text Box and then click Continue.

The total cost depends of the cost of the carpet, area, installation rate, and .

Review Statement 1 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

1) Carpet B takes one-third longer to install than carpet A.

Sufficient

Insufficient

Review Statement 2 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

2) Labor costs are $20 per hour.

Sufficient

Insufficient

Review the statements, and the equations we've built from them, in combination. Are they sufficient or insufficient? Select the correct answer and then click Continue.

1) Carpet B takes one-third longer to install than carpet A.

2) Labor costs are $20 per hour.

Sufficient

Insufficient

Countinue

Yep, we still don’t know which is greater, the difference in the cost of the carpet (1.5(area)) or the difference in the cost of the labor (20 times ). Now, if either carpet had higher costs than the other for both purchase and installation, then we’d be able to say which was more expensive overall. But because one has higher purchase costs and the other higher installation costs, and we don’t know exactly how many square feet will be used or how many hours it will take, we can’t know for sure which carpet will be more expensive in the end. So the statements are insufficient to answer the question.

You can see now that the mathematical operations in these last two questions were relatively straightforward. They didn’t require obscure formulae or tricky calculations, but they did require you to be able to reduce a situation to its components. So, if a Data Sufficiency question presents what at first appears to be a complex verbal situation (as opposed to complex math), take a step back and think about how you can reduce the problem to simple operations. Look for ways to visualize the math, as we did when we rewrote the problem as equations.

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