GMAT Rates Practice Questions

A regional agency assesses the energy efficiency of office buildings over a rating period of 20 consecutive days.

For one building, electricity use averaged 150 kilowatt-hours $kWh$ per day at the start of the period. An efficiency upgrade took effect at the beginning of one of the 20 days, and from that day through the end of the period, inclusive, use averaged 100 kWh per day. Each rate therefore applied for a whole number of days, and each rate was in effect for at least one day.

For rating purposes, the agency adjusts the building's total use for the period. It first increases the total by 20% to account for transmission losses, and it then decreases the resulting amount by 25% to credit the building's on-site generation. The adjusted total, divided by 20, is the building's adjusted average daily use.

The building's efficiency rating is defined as 20 times the amount by which the pre-upgrade rate of 150 kWh per day exceeds the adjusted average daily use. Given that the building's total electricity use for the 20 days was 2,600 kWh, what is the building's efficiency rating?

A worker uses a powered mechanism to raise a bucket from a fixed depth in a well. Each retrieval consists of a preparation period followed by the bucket's ascent at a constant speed. The preparation time and ascent distance are unchanged by upgrades to the mechanism. Each upgrade increases the ascent speed by the same percentage of the speed immediately before that upgrade.

The worker's log records total retrieval times of 30 seconds before any upgrades, 24 seconds after the first upgrade, and 20 seconds after the second upgrade. These times are exact, and the second upgrade has just been completed. Only whole upgrades can be made.

What is the minimum number of additional upgrades needed to make the total retrieval time at most 15 seconds?

A cyclist rides uphill and then on level ground with a dry bicycle chain. The cyclist travels at 12 miles per hour uphill and 18 miles per hour on level ground, completing the ride in 3 hours 10 minutes. After lubricating the chain, the cyclist rides the same route. The uphill and level distances are unchanged, but the cyclist's speed increases by 25% uphill and 50% on level ground. The time saved uphill compared with the dry-chain ride is to the time saved on level ground as 2 to 3. What is the total length of the route, in miles?

A city streets crew prunes curbside trees on a rotating schedule, and the crew's truck makes one round trip each workday between the depot and that day's pruning site. The round trip is 45 kilometers in all, and the lengths of the outbound route and the return route are in the ratio 2 to 1, with the outbound route longer. On the first day, the truck averages 30 kilometers per hour for the entire outbound leg and 60 kilometers per hour for the entire return leg, each speed constant across its leg, and no driving time is counted for the stop at the site. On the second day, the truck makes the identical round trip at a constant speed of 40 kilometers per hour in both directions. The truck's average speed for the round trip on the second day is how many kilometers per hour greater than its average speed for the round trip on the first day?

A bus route has 5 stops, labeled A, B, C, D, and E. The distance between consecutive stops increases by 1 mile each time, starting from A to B. What is the average distance, in miles, between all consecutive stops?

A runner plans to use a treadmill for two consecutive 3-mile segments without pausing. The planned belt speeds for the first and second segments are in a 3:4 ratio. For each segment, the treadmill runs at the planned speed if it is at most 10 miles per hour, but runs at 10 miles per hour if the planned speed is higher. The runner completes the 6 miles in 38 minutes. What was the planned belt speed for the second segment?

A distiller fills two barrels, A and B. Their initial volumes are in a 4:3 ratio, and their evaporation rates are in a 2:3 ratio. Each barrel loses liquid at its own constant rate, measured in liters per day, only while it contains liquid. Four days after filling, the barrels contain a total of 50 liters, and their remaining volumes are in a 16:9 ratio. How many days after filling will the combined volume first equal 1/7 of the combined initial volume?

A basketball team has made 120 of its 200 free throw attempts. Two players, A and B, will take all of the team's additional free throws, each at a constant number of attempts per minute.

In separate hypothetical continuations from this same team record, A alone would bring the team's cumulative free throw percentage to exactly 75% in 20 minutes, making exactly 90% of A's attempts during every complete minute. B alone would bring the team's cumulative percentage to exactly 75% in 30 minutes, making exactly 80% of B's attempts during every complete minute. Neither player's performance changes during these hypothetical continuations.

In the actual continuation, A and B begin shooting together at their respective attempt rates. Initially, A makes exactly 90% and B makes exactly 80% of their respective attempts during each complete minute. At the first whole-minute checkpoint when the team's cumulative percentage is at least 70%, A's performance changes: during every subsequent complete minute, A makes exactly 70% of A's attempts. B continues to make exactly 80%, and neither player's attempt rate changes.

All attempt counts and successful-shot counts in each complete minute are integers. The stated percentages are exact performance rates, not probabilities, and cumulative percentages are evaluated only at whole-minute checkpoints. How many minutes after the actual continuation begins will the team's cumulative free throw percentage first be at least 75%?

A payroll department processes transactions through 10 employees: 3 senior staff (each handling 30% of transactions with a 5% error rate), 5 junior staff (each handling 50% of transactions with a 10% error rate), and 2 trainees (each handling 20% of transactions with a 20% error rate). If one transaction is randomly selected, what is the probability it contains at least one error?