GMAT Algebra Practice Questions

A gardener trains pumpkin vines in two raised beds, a north bed and a south bed. Each vine is either tied to a trellis wire or left untied, and the gardener pinches off the growing tip of some vines so they stay within their allotted spacing, so each vine is also either pinched or not pinched.

At the start of the season the north bed had twice as many vines as the south bed. Partway through the season, 10 vines were transplanted from the south bed into gaps in the north bed to even out the spacing, and after this move the north bed had three times as many vines as the south bed. The transplanted vines are counted as north-bed vines from then on.

Of the vines now in the north bed, 50% are tied, 40% are pinched, and 40% are neither tied nor pinched. Of the vines now in the south bed, 50% are tied, 60% are pinched, and 10% are neither tied nor pinched. Every vine falls into exactly one of four categories: tied and pinched, tied only, pinched only, or neither, and all vine counts are whole numbers.

Of all the vines now in the two beds that are tied, what percent are also pinched?

At a community herb shed, members work independently, each pulling herb bundles at random from the shared storage bin and tying them in a row across a drying cord. Maya's cord is 100 cm long, and every bundle she ties is 8 cm wide at the tie point. She leaves a gap between each pair of adjacent bundles and also between each end bundle and the nearest end of the cord, and every gap is half as wide as a bundle. Filled this way, her cord holds a whole number of bundles with no cord left over. The shed sells each dried bundle for $50. Maya deposits all the revenue from her fully filled cord into an account paying 10% interest per year, compounded annually, and she makes no other deposits or withdrawals for 2 years. How much interest does the deposit earn during the second year?

A driverless service cart crosses the bus loading area of a transit terminal, moving in a straight line from the terminal building to the far edge of the apron. The loading area is 48 meters wide, and this width is split into three zones. A pedestrian zone occupies 1/4 of the width. A bicycle lane occupies 1/3 of the remaining width. The rest of the width is taken by the bus berths where buses load. The distance the cart covers in each zone equals that zone's width, and the cart's speed is constant within each zone. The cart moves at 2 meters per second in the pedestrian zone and at 4 meters per second across the bus berths. Its speed in the bicycle lane is v meters per second, where v is less than 2 and $v - 2$^2 = 1.

What is the cart's average speed, in meters per second, for the full crossing of the loading area?

A factory is comparing two shift-overlap policies. Under either policy, an overlap lasting h hours requires h extra workers throughout the overlap, adding h² extra worker-hours. The longer overlap adds 45 more extra worker-hours than the shorter overlap. Both overlaps last a positive whole number of hours. The longer overlap is at most 10 hours and lasts less than twice as long as the shorter overlap. What is the product of the two overlap durations, in square hours?

A neighborhood food co-op sends a van to a farm. The van drives 24 miles to the farm in 60 minutes and returns by a different route of 66 miles in 120 minutes. For the basil bunches and tomato cartons unloaded that day, the co-op uses a shelf life number d days. Let s be the van's average speed for the whole round trip, in miles per hour. The co-op's label rule says that d is the root of $d - s/10$^2 = 1 that is greater than the number of hours the van was gone. On the shelf, basil bunches and tomato cartons are in the ratio 2:3, and there are 50 of these items in all. For the tomato cartons, the percent that have at least d days of shelf life left is a whole number multiple of 10%, is as large as possible, and cannot exceed 10d%. The co-op tags these qualifying tomato cartons, each with at most one tag. At least one qualifying carton must get a yellow tag and at least one qualifying carton must get an orange tag. What is the greatest possible number of qualifying tomato cartons that can get a green tag?

A payroll department has 12 employees: 8 are trained in payroll software A, and 6 are trained in payroll software B. Each employee is trained in at least one software. If an employee is selected at random, what is the probability that they are trained in at least one of the two software programs?

A shopkeeper personalizes and wraps N gifts, numbered in the order completed from 1 to N. Personalizing gift 1 takes 3 minutes, and personalizing each subsequent gift takes 2 minutes longer than personalizing the preceding gift. Wrapping gift i takes exactly as long as personalizing gift N + 1 − i.

For some positive integer k less than N, completing the first k gifts takes 60 minutes in total. The time spent personalizing those k gifts is one-third of the time spent wrapping them. How many minutes does it take to wrap the gift immediately after the first k gifts?

A city residents association is allocating rebates for solar panels on the rooftops of its apartment buildings. The number n of owners eligible to vote on the rebate rules is not posted. If 5 fewer owners were eligible, the product of the actual number and the reduced number would be 84. The rules pass if at least 3/5 of all eligible owners vote yes. If 3/5 of the eligible owners is not a whole number, the minimum passing number is rounded up to the next whole owner. Exactly 2 of the eligible owners are certified solar installers. For phase 1, the association will choose a review panel with one fewer member than the minimum passing number. For phase 2, it starts with a panel equal to the minimum passing number, increases that planned size by 25%, and then reduces the new planned size by 20%. Every panel size must be a whole number, and if a percent adjustment produces a fractional final size, the size is rounded up to the next whole member. Each panel is chosen from all eligible owners, panel members are unordered, no owner fills more than one seat on the same panel, and each panel must include at least one of the 2 certified installers. The phases are separate, and the count for one phase does not change the count for the other. What is the sum of the number of possible phase 1 panels and the number of possible phase 2 panels?

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?