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The total price of 5 pounds of regular coffee

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The total price of 5 pounds of regular coffee

by AbeNeedsAnswers » Tue Apr 30, 2019 5:41 pm

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The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee?

(1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.

(2) The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

D

Source: Official Guide 2020
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by Ian Stewart » Wed May 01, 2019 2:32 am

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Since we're never given any information about price per pound, the numbers in "5 pounds" and "3 pounds" are just a distraction. All we're doing here is mixing some regular coffee and some decaf coffee. Say all the regular coffee costs $R and all the decaf costs $D. The stem tells us:

R + D = 21.5

If we reduce the price of the regular coffee by 10%, the new price will be 0.9R. Similarly, if we reduce the decaf coffee's price by 20%, the new price will be 0.8D. So Statement 1 tells us that

0.9R + 0.8D = 18.45

This equation, and the equation in the stem, are linear equations (i.e. we can rewrite them in the form y = mx + b), and they are distinct equations (we can't multiply one equation by some number to get the other equation), so if we were to graph them as two lines in the coordinate plane, they'd meet in exactly one point, and they thus have exactly one solution for R and D. Since this is a DS question, there's no reason to find the solution, and Statement 1 is sufficient.

Statement 2 tells us

R - D = 3.5

and again we have two distinct linear equations in two unknowns, and we can solve for R and D. So this is also sufficient and the answer is D.
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by Scott@TargetTestPrep » Tue May 07, 2019 5:29 pm

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AbeNeedsAnswers wrote:The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee?

(1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.

(2) The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

D

Source: Official Guide 2020
We can create the equation:

5r + 3d = 21.5

We need to determine 5r.

Statement One Alone:

If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.

We can create the equation:

5(0.9r) + 3(0.8d) = 18.45

4.5r + 2.4d = 18.45

45r + 24d = 184.5

Multiplying the equation in the stem analysis by 8, we have 40r + 24d = 172. Subtracting this from the equation above, we have:

5r = 12.5

Therefore, we see that the value of 5r is 12.5. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

We can create the equation:

5r = 3d + 3.50

3d = 5r - 3.50

Substituting 5r - 3.50 for 3d in the equation in the stem analysis, we have:

5r + 5r - 3.50 = 21.5

10r = 25

5r = 12.5

We see that the value of 5r is 12.5. Statement two alone is sufficient to answer the question.

Answer: D

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by [email protected] » Fri May 10, 2019 2:49 pm

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Hi All,

We're told that the total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. We're asked for the price of the 5 pounds of regular coffee. The information in the first sentence can be used to create a 2 variable equation, which should get us thinking about 'System math' (re: 2 variables and 2 unique equations):

5(R) + 3(D) = $21.50

R represents the price of a pound of regular coffee while D represents the price of a pound of decaffeinated coffee. If we enough information to create a second, unique equation using those 2 variables, then we can stop working - that information would be enough for us to get to the correct answer and solve for the prices/pound of the two coffees.

(1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.

The information in Fact 1 can be used to create another equation:

5(.9R) + 3(.8D) = $18.45

While the two equations might look a bit 'ugly', it's still a System of equations, so we CAN solve for the two variables. Thankfully, we don't actually have to do that work to know that we COULD, so we would know the exact value of 5R.
Fact 1 is SUFFICIENT

(2) The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

With the information in Fact 2, we can create an equation relating the values of 5R and 3D:

5R = 3D + $3.50

Again, we end up with a System of equations, so we CAN solve for the two variables. Thankfully, we don't actually have to do that work to know that we COULD, so we would know the exact value of 5R.
Fact 2 is SUFFICIENT

Final Answer: D

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