Data Sufficiency

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
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

[Show/hide explanation]

You're given the price of a typewriter and the price of a calculator. You're asked for the total cost of the typewriters and calculators, which can be written as 100 r + 50 s . Statement (1) tells you that the calculators cost $200. You can use this information to solve for s , but you can't find the total cost, so (1) is insufficient. Statement (2) tells you that 2 r + s = 10. Notice that the coefficients in the statement, 2 for r and 1 for s , are in the same ratio as the expression you derived from the stem. In fact, if you multiply both sides of the equation of statement (2) by 50, you'll get 100 r + 50 s = 500. This gives us the total cost of the calculators and typewriters, so (2) is sufficient.

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.)

Thanks -- your explanation makes a lot of sense.

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.)