Navigating Arithmetical Reasoning: A Comprehensive Example

Arithmetical Reasoning is a staple of many competitive exams, challenging test-takers to apply mathematical principles to solve logical puzzles. Unlike direct arithmetic problems, these questions are wrapped in real-world scenarios, requiring a blend of logical analysis and mathematical skill. Below, we delve into an example that showcases typical arithmetical reasoning challenges, followed by a detailed, step-by-step solution.

Example Problem: The Bakery Order

A bakery received an order for a party. The order included 3 types of pastries: croissants, muffins, and scones. The order had the following requirements:

• The number of muffins ordered was twice the number of croissants.
• The number of scones was 10 more than the number of muffins.
• The total order was for 90 pastries.

Determine the number of each type of pastry in the order.

Step-by-Step Solution:

Step 1: Represent the Information Algebraically

Let’s assign variables to the quantities we need to find:

• Let $C$ represent the number of croissants.
• The number of muffins is twice the number of croissants, so let $2C$ represent the number of muffins.
• The number of scones is 10 more than the number of muffins, so let $2C + 10$ represent the number of scones.

Step 2: Set Up the Equation

According to the problem, the total order was for 90 pastries. This gives us the equation:

$C + 2C + (2C + 10) = 90$

Step 3: Solve for $C$

Combine like terms:

$5C + 10 = 90$

Subtract 10 from both sides:

$5C = 80$

Divide by 5:

$C = 16$

Step 4: Find the Number of Muffins and Scones

• Since $C = 16$ , there were 16 croissants.
• The number of muffins, $2C$ , is $2 \times 16 = 32$ .
• The number of scones, $2C + 10$ , is $32 + 10 = 42$ .

Conclusion:

The bakery’s order consisted of 16 croissants, 32 muffins, and 42 scones to meet the requirement for 90 pastries.

Understanding the Solution

This example illustrates the application of basic algebra to solve an arithmetical reasoning problem. By translating the word problem into mathematical expressions and equations, we systematically find the solution. This approach is effective for various types of arithmetical reasoning questions encountered in competitive exams.

Arithmetical reasoning tests your ability to navigate numerical information and solve problems efficiently. It’s not just about crunching numbers but understanding the logical structure of the problem. Regular practice with these types of questions can greatly improve your problem-solving speed and accuracy, giving you a competitive edge.