All practice questions

A merchant purchased a shipment of 200 identical items for a total cost of $8,000. The merchant marked up the cost price of each item by$ P $percent to establish its list price. During the first month of sales, 60 percent of the items were sold at the list price. During the second month, 50 percent of the remaining items were sold at a 20 percent discount off the list price. The remaining items were then sold during a clearance sale at a 50 percent discount off the list price. If the merchant made an overall net profit of 29 percent on the total purchase cost of the shipment, what is the value of$ P$?

The scores of a student on five quizzes are $72, 85, 90, 78,$ and $95$. What is the positive difference between the median and the arithmetic mean of these five quiz scores?

A global logistics firm consists of three distinct divisions: Express, Freight, and Solutions. In a given fiscal year, the annual revenue per employee was $\$120,000$ for the Express division, $\$180,000$ for the Freight division, and $\$240,000$ for the Solutions division. The number of employees in the Freight division was $25\%$ greater than the number of employees in the Express division. If the overall weighted average revenue per employee across all three divisions combined was $\$180,000$, and the total annual revenue generated by the Solutions division was $\$14,400,000$, what was the total number of employees across all three divisions?

A ferry travels from Port Alpha to Port Beta across a bay, a distance of $30$ miles, at a constant speed of $15$ miles per hour. On the return trip from Port Beta to Port Alpha along the exact same route, the ferry travels at a constant speed of $30$ miles per hour. What is the ferry's average speed, in miles per hour, for the entire round trip?

A piece of industrial machinery valued at $\$5,000$ depreciates in value by $20\%$ during its first year of operation, and by $10\%$ of its reduced value during its second year. What is the value of the machinery, in dollars, at the end of the second year?

For how many integer values of $k$ does the equation $|x - 2| + |x + 4| = kx + 1$ have no real solutions for $x$?

Tank X initially contains $50$ liters of a solvent solution that is $20\%$ chemical compound by volume. Tank Y initially contains $30$ liters of a solvent solution that is $70\%$ of the same chemical compound by volume. First, $v$ liters of the solution in Tank X are transferred to Tank Y and thoroughly mixed. Then, $v$ liters of the resulting mixture in Tank Y are transferred back to Tank X. If the final concentration of the chemical compound in Tank X is $32\%$ by volume, what is the value of $v$?

A research team needs to select a subcommittee of 3 scientists from a department containing 7 scientists. How many different 3-member subcommittees can be selected?

In a certain training program, Class A has $15$ participants with an average score of $80$ on a final exam, and Class B has $25$ participants with an average score of $88$ on the same exam. What is the average score for all $40$ participants combined?

A financial consulting firm audited $500$ corporate investment portfolios for exposure to three alternative asset classes: Private Equity ($P$), Venture Capital ($V$), and Infrastructure ($I$). Every audited portfolio contained at least one of the three asset classes.

The audit revealed the following:
- Exactly $270$ portfolios contained Private Equity.
- Exactly $250$ portfolios contained Venture Capital.
- Exactly $220$ portfolios contained Infrastructure.
- The ratio of the number of portfolios containing both Private Equity and Venture Capital to those containing both Venture Capital and Infrastructure to those containing both Private Equity and Infrastructure was $11 : 9 : 10$, respectively.
- The number of portfolios containing all three asset classes was $60$.

How many portfolios contained exactly two of the three asset classes?

Two automated document redaction pipelines, Pipeline $A$ and Pipeline $B$, process digital legal archives. Working alone at its constant rate, Pipeline $A$ can redact a standard archive in $8$ hours. Working alone at its constant rate, Pipeline $B$ can redact the same standard archive in $12$ hours. Both pipelines begin processing a standard archive together. After $3$ hours of joint operation, Pipeline $A$ encounters a system error and stops. Pipeline $B$ continues working alone at its constant rate until the entire archive is redacted. How many total hours does it take from start to finish to complete the redaction of the archive?

A logistics company operates two models of cargo trucks, Model X and Model Y, to transport freight between two distribution hubs. Model X consumes $10$ liters of fuel per $100$ kilometers driven in city traffic and $6$ liters of fuel per $100$ kilometers driven on open highway. Model Y consumes $14$ liters of fuel per $100$ kilometers in city traffic and $8$ liters per $100$ kilometers on open highway. On a trip between the two hubs along a route composed entirely of city traffic segments and open highway segments, Model X consumed a total of $42$ liters of fuel, and Model Y consumed a total of $58$ liters of fuel. What is the total length, in kilometers, of the open highway segments along this route?

A logistics company operates a fleet consisting of standard electric delivery vans and high-capacity electric delivery vans. A standard van consumes a fixed $2.5$ kilowatt-hours (kWh) of electricity per delivery route, while a high-capacity van consumes $50\%$ more electricity per route than a standard van. On a given day, the fleet completed a total of $40$ delivery routes and consumed a total of $130$ kWh of electricity. How many delivery routes were completed by high-capacity vans?

Eight executive team members—3 vice presidents, 3 directors, and 2 managers—are to stand in a single line for a company photograph. If no two vice presidents can stand next to each other, and the 2 managers must stand next to each other, how many different linear arrangements of the eight team members are possible?

A board of directors consists of $7$ members. In how many different ways can a subcommittee of $3$ members be chosen from the board?

A dataset consists of 20 distinct numerical values arranged in increasing order. The lower quartile ($Q_1$) of the dataset is equal to the average of the 5th and 6th values, and the upper quartile ($Q_3$) is equal to the average of the 15th and 16th values. Given that the lower quartile $Q_1 = 42$, the interquartile range ($\text{IQR} = Q_3 - Q_1$) is 38, and the 15th value in the dataset is 74, what is the value of the 16th term?

Set $S$ consists of five distinct integers: $14, 22, 18, 9,$ and $31$. What is the range of the numbers in Set $S$?

A dataset contains $20$ distinct test scores arranged in ascending order:

$10, 12, 15, 17, 20, 22, 25, 28, 30, 32, 35, 38, 40, 43, 45, 48, 50, 52, 55, 60$

If the $p\text{th}$ percentile of a dataset of $N$ values is defined as the value at position $k = \frac{p}{100} \times N$ when ordered from least to greatest, what is the $75\text{th}$ percentile of these test scores?

An investment fund allocated its total capital into three distinct asset classes: Class X, Class Y, and Class Z. Class X yielded an annual return of $12\%$, Class Y yielded an annual return of $18\%$, and Class Z yielded an annual return of $6\%$. The capital invested in Class X was exactly twice the capital invested in Class Y. If the overall weighted annual return for the entire fund was $11\%$, what percentage of the total capital was invested in Class Z?

A merchant blends two types of coffee beans: Type A, which costs $\$12$ per kilogram and contains $15\%$ caffeine by weight, and Type B, which costs $\$18$ per kilogram and contains $25\%$ caffeine by weight. The merchant mixes Type A and Type B to create a $60$-kilogram batch of Blend C. If the total cost of the $60$-kilogram batch of Blend C is $\$936$, what is the percentage of caffeine by weight in Blend C?