Question

A baseball card collector has 1,100 cards that are in mint condition and 400 cards that are not. Of those cards in mint condition, 60 percent are rookie cards. If 740 of the cards in his collection are not rookie cards, then how many cards in the collection are rookie cards that are not in mint condition?

Short answer

100 cards.

Step-by-step solution

Total Rookie Cards

Calculate the total number of rookie cards in the collection. Subtract the total number of non-rookie cards (740) from the total number of cards.Total Cards: 1100 (mint) + 400 (not mint) = 1500 cards.Total Rookie Cards: 1500 - 740 = 760 rookie cards.

Mint Rookie Cards

Find the number of rookie cards that are in mint condition. Multiply the number of mint condition cards by 60%.Mint Rookie Cards = 0.60 * 1100 = 660 cards.

Non-Mint Rookie Cards

Subtract the number of rookie cards in mint condition from the total number of rookie cards to find the number of rookie cards that are not in mint condition.Non-Mint Rookie Cards = Total Rookie Cards - Mint Rookie Cards= 760 - 660 = 100 cards.

Key concepts

Percentage Calculation

Percentage calculation is a crucial part of many GMAT math problems. In this exercise, we found that 60 percent of the mint condition cards are rookie cards. To calculate this:

First, identify the total number of mint condition cards, which is 1,100 cards.

Then, multiply by the percentage (60%) to find the number of rookie cards in mint condition:

\[1100 \times 0.60 = 660 \text{ mint rookie cards} \]

Always convert the percentage into decimal form by dividing by 100 before multiplying. This helps to ensure accurate calculations.

Understanding percentage calculation is key in problem-solving as it often represents a significant portion of the whole, which is necessary for deriving other values.

Subtraction

Subtraction is another core concept used in this problem-solving process.


Initially, we needed to determine the total number of rookie cards in the collection. To do this, we subtracted the number of non-rookie cards (740) from the total number of cards (1,500):

\[1500 - 740 = 760 \text{ rookie cards} \]

Finally, we found the number of rookie cards that are not in mint condition by subtracting the number of mint rookie cards from the total rookie cards:

\[760 - 660 = 100 \text{ non-mint rookie cards} \]

Subtraction helps isolate the quantities we need by removing any known values from the total, revealing the unknown values we seek.

Total Calculation

In this exercise, calculating the total of different parts is fundamental.

First, we need the overall total of baseball cards:

\[1100 \text{ (mint)} + 400 \text{ (not mint)} = 1500 \text{ cards} \]

Knowing how to sum parts to find the total is essential for understanding the big picture.

Once we have the total, we can manipulate it further to extract meaningful information by applying different operations, like percentage calculations and subtractions.

Problem-Solving Strategy

A good problem-solving strategy is essential for efficiently tackling any exercise. Here’s how you can approach similar problems:

• Understand the problem: Carefully read the question to understand what is being asked.

• Break it down: Divide the problem into manageable steps. Identify which details are given and what needs to be found.

• Analyze and calculate: Use mathematical operations (addition, subtraction, multiplication, percentage calculations) step by step to solve the problem.

In our example, we:

• First found the total number of cards.
• Then calculated the total number of rookie cards.
• Next, determined the number of rookie cards in mint condition using percentage calculation.
• Finally, we subtracted the mint rookie cards from the total rookie cards to find the non-mint rookie cards.
Following these strategic steps makes problem-solving structured and more manageable.