Mastering Internship Math Assessments

Operations, Productivity, and Unit Costs

In operations, supply chain, or warehouse-focused internships, you will often encounter questions regarding efficiency and cost-effectiveness.

• Averages: To find the average (such as average daily sales), sum all values and divide by the total number of values.
• Unit Cost: This is calculated as $\frac{\text{Total Cost}}{\text{Number of Units}}$. This metric is vital when comparing suppliers; a lower total cost does not always mean a better deal if the unit cost is higher.
• Productivity: This measures output over time, calculated as $\frac{\text{Output}}{\text{Time}}$. For example, a warehouse processing 360 boxes in 6 hours has a productivity of 60 boxes per hour.

Retail Math: Profit, Markup, and Margin

Retail math requires careful attention to detail, particularly when dealing with multiple steps like discounts or distinguishing between profit margin and markup.

Discounts and Sales Tax

When applying a discount, you can either find the discount amount and subtract it from the original price, or multiply the original price by the remaining percentage. For a $30%$ discount, you simply pay $70%$ of the price ($100% - 30% = 70%$).

For sales tax, calculate the tax amount and add it to the price, or use the shortcut of multiplying the price by $(1 + \text{Tax Rate})$.

Profit, Margin, and Markup

A common pitfall is confusing Profit Margin with Markup. While both use the profit amount (Selling Price $-$ Cost), their denominators differ:

1. Profit Margin: Compares profit to the Selling Price. $\text{Profit Margin} = \frac{\text{Profit}}{\text{Selling Price}} \times 100$
2. Markup: Compares profit to the Cost. $\text{Markup} = \frac{\text{Profit}}{\text{Cost}} \times 100$

Warning on Multiple Discounts: If a product has a $20%$ discount followed by a $10%$ discount, do not simply add them to get $30%$. You must apply the second discount to the already reduced price.

Data Literacy and Supplier Comparisons

Data literacy involves interpreting tables to make business decisions. You may be presented with multiple suppliers and asked to choose the "best" option based on metrics like unit cost and defect rates.

In these scenarios, there is often no single "correct" answer based on one metric alone. For instance, one supplier might offer the lowest cost per unit, while another offers the lowest defect rate. A successful candidate must weigh these conflicting data points against business requirements like quality and reliability.

Ratios and Proportions

Ratios are used to divide totals into specific shares. To divide a total into a ratio of $a:b$, follow these three steps:

1. Sum the ratio parts ($a + b$).
2. Divide the total by that sum to find the value of one "part."
3. Multiply each ratio number by the value of that single part.

For example, to divide $$600$ in a $2:3$ ratio:

• Total parts: $2 + 3 = 5$
• Value per part: $\text{\textdollar}600 \div 5 = \text{\textdollar}120$
• Shares: $2 \times \text{\textdollar}120 = \text{\textdollar}240$ and $3 \times \text{\textdollar}120 = \text{\textdollar}360$.

Logical Reasoning and Patterns

The final component of many assessments is IQ-style logic, which tests your ability to identify rules rather than just performing calculations.

Number Sequences

Look for two primary types of patterns:

• Multiplication Patterns: Where each number is multiplied by a constant (e.g., $3, 6, 12, 24 \dots$ where each is $\times 2$).
• Increasing Differences: Where the amount added to each number grows (e.g., $2, 5, 9, 14 \dots$ where you add $3, 4, 5 \dots$).

Logical Deduction and Ordering

• Logical Statements: Use only the provided premises. If a statement says "All Lums are blue," you cannot assume "Some Lums are large" unless the text explicitly states it.
• Ordering Questions: Use relational statements to build a sequence. If Alex finishes before Blair, and Casey finishes after Blair, the order must be Alex $\rightarrow$ Blair $\rightarrow$ Casey.

By mastering these formulas and logical frameworks, you will be better equipped to navigate the complexities of your internship assessment with speed and confidence.