Graduate Management Admission Test (GMAT) Practice Test

What two conditions must be satisfied for a number to be divisible by 12?

1. Divisible by 2 and 6

2. Divisible by 3 and 5

3. Divisible by 3 and 4

4. Divisible by 6 and 4

The correct answer is: Divisible by 3 and 4

For a number to be divisible by 12, it must meet specific criteria based on its factors. The fundamental concept here involves breaking down 12 into its prime factors. The number 12 can be expressed as \(2^2 \times 3\), meaning that it encompasses the factors 2 and 3. To determine divisibility, a number must be divisible by both 4 and 3. Divisibility by 4 ensures that the number has enough factors of 2 (specifically at least two 2's), while divisibility by 3 ensures that the number can accommodate the factor of 3 present in 12. This understanding leads us to recognize that meeting these criteria together guarantees that the number is divisible by 12, as satisfying the conditions for both 4 and 3 collectively covers all prime factors of 12. Thus, a number divisible by 3 and 4 is indeed divisible by 12.