GMAT Number Properties Practice Questions

A software company offers monthly subscriptions that renew on the same day each month. If the number of subscriptions is divisible by 7 and leaves a remainder of 0 when divided by 10, what is the smallest possible number of subscriptions?

In a laboratory experiment, two samples of a chemical solution are prepared from a total volume of $V$ liters, where $V$ is a whole number between 100 and 200. Sample A contains $\frac{5}{8}$ of the total volume, and Sample B contains $\frac{3}{10}$ of the total volume. The remaining solution is discarded. If the discarded volume must be an integer number of liters, what is the minimum possible volume of the discarded solution?

A university library is cataloging books for a special collection. Each book is assigned a unique 3-digit code where each digit is a prime number $2, 3, 5, or 7$. The codes are assigned sequentially starting from the smallest possible code (222) in numerical order. If the library has exactly 48 books in this collection, what is the code assigned to the 48th book?

A hospital wing has patient rooms numbered consecutively from 327 to 428. If each room number is increased by 4, how many of the new numbers must be divisible by 3?

The city charges each household a stormwater runoff fee based on how much rainwater drains from its roof and driveway into the street, and installing a rain barrel reduces that fee. A hardware store sells rain barrels during a two week sale. The store's cost is $40 per barrel. The regular price is the cost marked up by 60%, and the sale price is the regular price discounted by 25%. Every barrel sold during the sale is sold at the sale price.

During the first week the store sold barrels on 5 days. The numbers sold on the 5 days were 5 different consecutive integers, and the average (arithmetic mean) number sold per day was 12.

During the second week the store sold barrels on 4 days. The number sold on each of the 4 days was a different integer, at least one barrel was sold on each day, and the total number sold during the second week was equal to the number sold on the busiest day of the first week, that is, the day on which the most barrels were sold.

What is the greatest possible total profit, in dollars, from the barrels sold on the busiest day of the first week and the busiest day of the second week combined? (Profit per barrel is the sale price minus the cost.)

A film's box office revenue is tracked on consecutive days. On each day, the revenue is recorded as an integer amount (in millions). The sum of revenues over 11 consecutive days is 47. If the revenue on the first day was even, what is the maximum number of odd daily revenues possible in this sequence?

A library tracks the circulation periods for two categories of books: popular titles are due back in 12 days, while reference materials are due in 18 days. If a librarian checks out one popular title and one reference book on the same day, and the library operates every day of the week, how many times in the next 360 days will both books be due on the same day?

A city's charter includes a peculiar fiscal rule for funding public works. For any set of $N$ identical projects undertaken in a year, the square of the number of projects, $N^2$, must be divisible by the city's fiscal index, which is 2,940. If $N$ must be a positive integer, what is the largest possible integer that must be a factor of $N$?

A library assigns unique identifiers to books: each fiction book's identifier is the product of three distinct primes, and each non-fiction book's identifier is the product of two distinct primes. A shelf identifier is the product of all book identifiers on that shelf. If a shelf contains exactly 2 fiction books and 3 non-fiction books, what is the minimum number of distinct prime factors the shelf identifier can have?