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## OG 2020: Question No. 315

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.

### Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was \$21.50.

We need to determine

• The price of the 5 pounds of regular coffee.

If we assume that the price of 1 pound of regular coffee was R and 1 pound of decaffeinated coffee was D, then as per the given information, 5R + 3D = 21.5

To find the value of 5R, we need to know

• Either the value of R
• Or, the value of D
• Or, the value of 3D

With this understanding, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

As per the information given in statement 1, if the price of 5 pounds of regular coffee had been reduced 10% and the price of 3 pounds of decaffeinated coffee had been reduced 20%, then the total price would have been \$18.45.

• Price of 5 pounds of regular coffee, after reducing by 10% = 0.9 × 5R = 4.5R
• Price of 3 pounds of decaffeinated coffee, after reducing by 20% = 0.8 × 3D = 2.4D
• Therefore, we can write 4.5R + 2.4D = 18.45
• We also know 5R + 3D = 21.5

Solving these two simultaneous equations, we can determine the individual value of R, and hence, can determine the value of 5R.

Hence, statement 1 is sufficient to answer the question.

#### Step 4: Analyse Statement 2

As per the information given in statement 2, the price of the 5 pounds of regular coffee was \$3.50 more than the price of the 3 pounds of decaffeinated coffee.

• Therefore, we can write 5R = 3.5 + 3D

Or, 5R – 3D = 3.5

• We also know that 5R + 3D = 21.5

Solving these two simultaneous equations, we can determine the individual value of R, and hence, can determine the value of 5R.

Hence, statement 2 is sufficient to answer the question.

#### Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.

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