GMAT Ratios Practice Questions

A library's book return system tracks volumes using exponents. On Monday, returned books were at a rate of $2^{x}$ per hour while checked-out books were $2^{x}$ per hour. On Tuesday, returned books changed to $2^{x+1}$ per hour while checked-out remained $2^{x}$. On Wednesday, returned books were $2^{x}$ per hour while checked-out became $2^{x+1}$. What is the ratio of Tuesday's return volume to Wednesday's return volume?

A library tracks book circulation using integer ratios in lowest terms. For a particular book, the ratio of checkouts to returns this month is 4:5, and the ratio of new acquisitions to withdrawals is 3:2. If the net change in inventory is calculated as (checkouts - returns) × (new acquisitions - withdrawals), what is the sign of this change?

A community radio station streamed a 50-minute concert on its website. Each listener received either a standard stream at a bitrate of 64 kilobits per second or a high-quality stream at a bitrate of 256 kilobits per second, and no listener changed streams during the concert. Because of a server limitation, the high-quality stream was available only during the final 25 minutes of the concert; each high-quality listener streamed exactly those 25 minutes, while each standard listener streamed the full 50 minutes. Streaming at a bitrate of 1 kilobit per second for 1 minute consumes 7.5 kilobytes of bandwidth, and 1000 kilobytes equal 1 megabyte. The ratio of the number of standard listeners to the number of high-quality listeners was exactly 3 to 5, and the total number of listeners was at least 74, where at least 74 means 74 or more. If the total number of listeners was the smallest whole number consistent with all of these conditions, what was the total bandwidth consumed by all the listeners, in megabytes?

A construction project requires 2.5 cubic meters of concrete per floor. The project has a total budget of 12,500 dollars for concrete, and the supplier charges 0.80 dollars per cubic decimeter. How many floors can be constructed without exceeding the budget? (1 cubic meter = 1,000 cubic decimeters.)

A city is replacing fixtures on the 240 streetlights along one avenue, numbered consecutively from 1 through 240. Each light will get a new LED head, a motion sensor, or both. LED heads are installed on every third light, starting with light 3. The LED head budget and the motion sensor budget are in the ratio 3:11, and the LED head budget is $15,000. A motion sensor costs $250 per light. How many lights get both a new LED head and a motion sensor?

A grower uses air pumps to supply nutrient tanks in two zones of a hydroponic growing room. Every pump is either a smaller model or a larger model, and their rated air capacities are in the ratio 3:5. All pumps of the same model have the same rated capacity, and a zone's combined rated capacity is the sum of its pumps' rated capacities.

Initially, the ratio of the number of pumps in zone A to the number in zone B is 4:3, and the ratio of their combined rated capacities, A to B, is 7:6. The grower exchanges one smaller pump from zone A with one larger pump from zone B, making no other changes. After the exchange, the ratio of the combined rated capacities, A to B, is 6:5.

What is the least possible total number of pumps in the two zones?

At a ski rental shop, every pair of boots in the opening inventory is either small-size or large-size. Each pair belongs to exactly one of three groups: pairs dried in the first batch, pairs dried in the second batch, or pairs still awaiting drying.

The ratio of small-size pairs to large-size pairs was 2:3 in the first batch and 3:4 in the second batch. The two batches contained the same number of small-size pairs. Among the pairs still awaiting drying, the ratio was 4:5. In the entire opening inventory, the ratio was 3:4.

There were 12 more pairs still awaiting drying than were dried in the first batch. How many pairs were in the opening inventory?

A city installs streetlights along a straight 900-meter street in three successive layouts. Each layout has a light at both endpoints and divides the street into a whole number of equal segments. From the initial to the second layout, the spacing between lights increases by 25%. From the second to the final layout, the spacing increases by 20% of the second layout's spacing. Exactly 14 positions strictly inside the street have a light in both the initial and final layouts. What is the spacing between lights in the final layout?

On Cedar Block, the city posts temporary no parking signs before the sweeper passes, and the block association sends one ballot to each household that had a car in the posted zone during last month's sweep. The sweeper clears the north side first and then the south side, but every returned ballot goes into one box and is counted only as yes or no. This month, returned ballots from north side households are 25% higher than last month, returned ballots from south side households are 50% lower than last month, and total returned ballots are 10% lower than last month. The renewal rule passes only if yes votes are more than 3/4 of this month's returned ballots. Ballots are whole, and the smallest number of yes votes that can pass is 41. How many south side households returned ballots last month?