DS - Word Problem

willshu wrote:The following question is from a Kaplan CAT. I do not agree with the answer, can someone see if they agree or disagree? To me (2) is simply a ratio that doesn't indicate the total cost of typewriters and calculators, but please let me know if you disagree.

A business bought r typewriters at $100 per typewriter and s calculators at $50 per calculator. What is the total cost of the typewriters and calculators?

(1) The s calculators cost $200

(2) 2 r + s = 10

Stuart Kovinsky wrote:

willshu wrote:The following question is from a Kaplan CAT. I do not agree with the answer, can someone see if they agree or disagree? To me (2) is simply a ratio that doesn't indicate the total cost of typewriters and calculators, but please let me know if you disagree.

A business bought r typewriters at $100 per typewriter and s calculators at $50 per calculator. What is the total cost of the typewriters and calculators?

(1) The s calculators cost $200

(2) 2 r + s = 10

Since it's a Kaplan question, let's use the Kaplan 3-step method for DS!

Step 1 of the Kaplan Method for DS: Focus on the question stem

We need the total cost of the objects. We see that a common formula applies, so let's start by jotting that down:

Total Cost = price(1)*quantity(1) + price(2)*quantity(2) + price(3)*quantity(3) + ...

Plugging our info in:

Total Cost = 100r + 50s

Many people would stop there (well, many people wouldn't even get thar far!), but if we go one step further this question becomes a snap:

Total Cost = 50(2r + s)

To summarize:

we have 3 variables and 1 equation. To solve, we either need 2 more distinct linear equations or 1 special equation that eliminates both variables we don't want (r and s).

Step 2 of the Kaplan Method for DS: Consider each statement by itself

(1) total cost of the calculators is $200.

Well, that eliminates the "s" from our equation, but still leaves us with 2 variables: total cost and r... insufficient!

(2) 2r + s = 10

For those who didn't break down the question as we did in step 1, this may seem like just another generic equation, leaving us with 2 equations and 3 unknowns. Those people would think (2) were insufficient.

However, our equation is:

Total Cost = 50(2r + s)

Now that we know that 2r + s = 10, we can simply sub that into our equation to get:

Total cost = 50(10), which certainly gives us a specific value for total cost... sufficient!

(2) is sufficient alone, (1) isn't: choose B.

(For those of you on the edge of your seats wondering about Step 3 of the Kaplan Method for DS, it's "if necessary, combine the statements". On this question one of the statements was sufficient by itself, so there's no need for combination.)