Graduate Management Admission Test (GMAT) Practice Test

If the remainder of n divided by 3 is 1, what can be inferred about n?

1. n = 3x + 1

2. n is divisible by 3

3. n = 3x

4. n is an odd number

The correct answer is: n = 3x + 1

When the remainder of a number \( n \) divided by 3 is 1, it indicates a specific relationship between \( n \) and its multiples of 3. The mathematical expression that captures this relationship is \( n = 3x + 1 \), where \( x \) is an integer. This equation shows that \( n \) can be expressed as some multiple of 3 (which is \( 3x \)) plus an additional 1. This equation highlights the structure of \( n \) clearly. For instance, if \( x = 0 \), \( n \) would equal 1; if \( x = 1 \), \( n \) would equal 4; if \( x = 2 \), \( n \) would be 7; and so forth. Each of these outcomes confirms that the remainder is indeed 1 when \( n \) is divided by 3. In contrast, the choice of whether \( n \) is divisible by 3 does not hold, as this would imply a remainder of 0, contradicting our initial condition. Likewise, \( n = 3x \) cannot be true since it suggests that \( n \) would have no remainder when