Question

A bookstore will only order books that come in complete cases. Each case has 150 books and \(\operatorname{costs} \$ 1,757\) Quantity \(\mathbf{A}\) The number of books that can be ordered for \(\$ 10,550\) Quantity \(B\) The number of books that can be ordered for \(\$ 12,290\) A. Quantity A is greater. B. Quantity B is greater C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Short answer

B. Quantity B is greater

Step-by-step solution

Calculate Quantity A

First, calculate how many complete cases can be bought with $10,550. As each case costs $1,757, the quantity can be calculated by dividing $10,550 by $1,757. Only complete cases can be ordered, so discard any decimal points. This gives the number of complete cases, which then need to be multiplied by the number of books per case (150). This gives the total number of books that can be ordered for $10,550.

Calculate Quantity B

Next, calculate how many complete cases can be bought with $12,290. Using the same method as in Step 1, divide $12,290 by $1,757 to get the number of complete cases. Discard any decimal points. Multiply this number by 150 to get the total number of books that can be ordered for $12,290.

Compare Quantities

Finally, compare the two quantities of books calculated in Steps 1 and 2. Whichever quantity is larger determines the answer to the problem.

Key concepts

Problem-Solving in Quantitative Reasoning

In the realm of GRE Quantitative Reasoning, problem-solving involves breaking down a problem into manageable steps and systematically finding a solution. Here, the bookstore scenario is a perfect example. Given specific resources and constraints—money available and complete cases required—you need to find a practical solution. One begins by identifying how many complete cases of books can be purchased with a given amount of money. You don't just divide the total money by the cost per case; you also make sure that the result is a whole number, as only complete cases can be ordered. This requires you to:

• Divide the total budget by the cost per case.
• Disregard any remainder to ensure full case purchases.
• Multiply the number of complete cases by the books per case to find the total books.

Applying these steps helps to solve the problem efficiently, ensuring that all aspects of the problem have been considered.

Mathematics of the Problem

Mathematics in this exercise focuses on basic operations like division and multiplication. Given the cost per case and the budget, you need to apply simple division to determine how many cases you can buy. Each calculation step requires careful attention to detail:

• Using division to find how many times the cost of one case fits into the total budget.
• Eliminating the decimal or remainder, since this represents incomplete cases you can't purchase.
• Multiplying the number of cases by the number of books per case to find your total order.

These operations not only check straightforward arithmetic but also require understanding of practical applications, as only full cases are permissible in the order.

Understanding Quantitative Comparisons

Quantitative comparisons are crucial when determining relationships between groups of numbers or items. With choices such as "Quantity A is greater" or "The two quantities are equal," it's all about comparing two calculated values based on presented constraints:

• Compute separate values for both quantities, using the given conditions.
• Compare the total number of books ordered for two different budget scenarios.
• Determine which quantity is greater or if the quantities are equal.

In many exercises, clear understanding and precise calculation lead directly to the solution classifying the larger or equal quantity. These comparisons require not just mathematical operations but also a clear logical approach to match quantities, considering any stipulated conditions.