GMAT Inequalities Practice Questions

A research facility has rectangular laboratories with integer side lengths (in meters) and areas of exactly 840 m². Each lab's width must be at least 5 m and its length must not exceed 50 m. How many distinct laboratory configurations meet these requirements?

A recycling center processes bottles in bags that each hold exactly 7 bottles. A shipment contains between 50 and 60 bottles. If the center has exactly 3 more bottles than needed to completely fill all its bags for this shipment, what is the total number of bottles in the shipment?

A train station's luggage locker room collects $840 in rental fees every week. The manager is saving to replace the old lockers with a new bank of lockers that can hold larger suitcases, priced at $9,000. At the end of each week, she deposits 1/4 of that week's fees into a savings fund, and then she deposits 1/3 of the remainder of that week's fees into the same fund. The fund earns no interest, and she makes no other deposits. She will order the new lockers as soon as the fund contains at least $9,000, where at least means $9,000 is enough. However, the supplier accepts an order only when the total number of weekly deposits the buyer has made is a prime number. What is the least number of weeks she must save in order to place the order?

A logistics company is optimizing delivery routes and finds that the travel time for a certain route is at least 2 hours but no more than 5 hours. The company also knows that the distance of the route is between 120 miles and 180 miles. If the average speed for the route is represented by $s$ miles per hour, which of the following inequalities must be true for all possible valid combinations of time and distance?

A fence crew is setting posts for a straight pasture run. The run's length in meters is 6 times the number of different unordered pairs of gate posts that can be chosen from the 9 painted posts on the rack. The spacing standard requires a post at each end of the run and requires each gap from one post to the next to be no more than 8 m; both end posts are counted, and the run length is measured from the first post to the last post. In a 240 minute work window, Rui sets one post in 10 minutes and works the whole window. Bea sets one post in 15 minutes, joins x minutes after the window starts, and then works until the window ends. They work independently at constant rates, only whole posts count, and x is a number of minutes from 0 to 240 inclusive. What is the latest possible value of x for the crew to set enough posts for the run?

A farm cooperative keeps $3,000 in a fund for a windmill that lifts water to a cattle tank. It spends 1/4 of the fund on tower repairs, then puts 1/3 of the remainder into a repair reserve, and leaves the rest as valve money. With this valve money the cooperative will buy exactly 7 valves, each either brass or steel. A brass valve costs $300 and a steel valve costs $100. The numbers of valves are whole numbers, the cooperative buys at least one steel valve, and it may spend up to the valve money but not more, with equality allowed. Three of the purchased valves will later be assigned at random to the intake, booster, and outlet ports; all assignments of three different valves to those named ports are equally likely, and the other four valves are unused. Water goes through the intake port, then the booster port, then the outlet port, so the same three valves in a different port order are a different installation. For an installation, let k be the number of brass valves in the intake and booster ports only. The pumping rate is 9 times 2^k liters per minute, and a rate of exactly 18 liters per minute counts. What is the greatest possible value of the probability that the rate is at least 18 liters per minute?

To prepare for the lunchtime rush, a hospital cafeteria makes two types of meal trays in complete standardized batches. Each type A batch produces 4 trays and uses 3 units of ingredient P and 1 unit of ingredient Q. Each type B batch produces 3 trays and uses 1 unit of P and 3 units of Q.

The cafeteria has 22 units of P and 22 units of Q available. The number of batches of each type must be a nonnegative integer. Ingredients may be left unused, all other supplies are sufficient, and demand is sufficient for every tray prepared. What is the greatest total number of meal trays the cafeteria can prepare?

A film studio tracks the box office performance of its films over consecutive weeks. For a sequence of consecutive weeks, the total box office revenue is 42 million. If the revenue increases by 1 million each week and the revenue in the first week is at least 10 million, how many such sequences are possible?

A coffee shop is comparing how many identical orders its staff completes with background music and with silence. In each equal-length work block, the staff completes a constant positive integer number of orders with music and a constant positive integer number with silence. These two numbers are the same for every schedule. Outputs from separate blocks add, and switching between music and silence has no effect on output.

A schedule consisting of 3 blocks with music and 2 blocks with silence produces fewer than 100 orders. A schedule consisting of 2 blocks with music and 3 blocks with silence produces more than 89 orders.

What is the greatest possible number of orders completed in a schedule consisting of 4 blocks with music and 1 block with silence?