GMAT Combinatorics Practice Questions
Combinatorics questions show up frequently in the quantitative section of the GMAT Focus Edition. They test your ability to count arrangements and selections using permutations and combinations. Below are practice questions taken from our bank to help you prepare.
Starter questions
These are sample questions to ease you into the topic. They cover the basic principles and the simplest forms these questions can take.
A telecom company calculates a customer's monthly bill using the formula:
where is the number of calling minutes used, is the number of messages sent, and is the data consumed in MB. and are positive integer exponents determined by the plan. For a particular plan, and satisfy both and . If a customer has used exactly 100 calling minutes, 200 messages, and 400 MB of data, how many distinct pairs of positive integers satisfy these conditions?
A construction firm is building a continuous 180-meter-long security fence for a new data center. The fence is to be made from a series of identical, uniform panels placed end-to-end, with no gaps or overlaps. For structural stability, engineering standards require that the length of each individual panel be an integer number of meters and greater than 3 meters but less than 20 meters. How many different possible lengths are there for the panels?
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More questions
These are examples that are more reflective of the exam. They include a couple of different steps and test the same concepts in slightly less obvious ways.
A restaurant offers a lunch special where customers can choose 1 main dish from 3 options, 1 side dish from 4 options, and 1 drink from 2 options. The manager decides to add an additional drink option, bringing the total number of drink choices to 3. How many different lunch special combinations can customers now order?
A small business has 8 employees: 3 are managers and 5 are associates. The business needs to form a committee of 3 employees, with the condition that the committee must include at least one manager. How many different committees can be formed?
A venture capital firm is selecting a 4-person leadership team from a group of 8 partners. The team will consist of one President, one Vice President, and two indistinguishable Managing Directors. How many different leadership teams can be formed?
A mission director is scheduling the launch of 6 distinct satellites, designated S, W, G, N, H, and B. The satellites are launched one at a time in a sequence. Due to orbital requirements, satellite N must always be launched last. Furthermore, satellite G must be launched immediately before satellite B. How many different valid launch sequences are possible under these constraints?
Hard questions
These are 705+ level questions that you can expect from the GMAT Focus Edition. They test multi-step reasoning, complicated word problems, and the hardest percent concepts the exam covers.
A company is assigning unique identification numbers to its employees. Each ID number consists of a sequence of 6 digits, where the first digit cannot be zero and no digit can be repeated. To ensure security, the company requires that the first digit must be greater than the last digit. How many distinct ID numbers can be assigned under these conditions?
A software company is planning a sequence of 6 product demonstrations for a major client. The demonstrations cover three distinct software modules: Analytics, Backend, and User Interface. There are to be exactly two demonstrations for each module. For the schedule to be effective, company policy dictates that exactly one of the three pairs of same-topic demonstrations can be scheduled consecutively. How many different valid schedules of the 6 demonstrations are possible?
A metro system tracks train speeds as 3-digit whole numbers in km/h. The sum of a speed's digits must equal 12, and none of its digits can be zero. How many possible speed values satisfy these conditions?
A company is assigning unique identification numbers to its employees. Each ID number consists of a sequence of 6 digits, where the first digit cannot be zero and no digit can be repeated. To ensure security, the company requires that the first digit must be greater than the last digit. How many distinct ID numbers can be assigned under these conditions?