GRE Arithmetic Practice Questions

Quantity A: The number of distinct prime factors of 42 Quantity B: The number of distinct prime factors of 60

Quantity A: The number of distinct prime factors of 42 Quantity B: The number of distinct prime factors of 60

Quantity A: The number of distinct prime factors of 30 Quantity B: The number of distinct prime factors of 42

Quantity A: The number of positive divisors of 36 Quantity B: The number of positive divisors of 48

Quantity A: The number of positive divisors of 36 Quantity B: The number of positive divisors of 48

Quantity A: The number of distinct prime factors of 36 Quantity B: The number of distinct prime factors of 48

A library surveyed 150 users about their borrowing habits. 80 users borrowed fiction books, 70 borrowed non-fiction books, and 20 borrowed neither type. How many users borrowed at least one type of book?

A city's annual budget must be allocated to three departments in the exact proportions of $\frac{1}{12}$, $\frac{1}{15}$, and $\frac{1}{20}$ of the total budget. If the allocation to each department must be a whole dollar amount, what is the smallest possible total budget that satisfies these conditions?

A city's budget must allocate funds in whole dollar amounts. The transportation department requires exactly $\frac{3}{4}$ of its allocation to be an integer, while the parks department requires exactly $\frac{5}{6}$ of its allocation to be an integer. What is the smallest possible total budget that satisfies both conditions?

A budget allocation is a positive integer between 200 and 300 that must be divisible by both 15 and 28. What is the minimum number of distinct prime factors any valid allocation can have?