BTGModeratorVI wrote: ↑

Mon Jun 08, 2020 12:00 pm

If m and n are prime numbers, is the remainder when 3m is divided by n greater than 5?

(1) m <10
(2) n < 6

Answer: B
Source: Economist GMAT

Target question: When 3m is divided by n, is the remainder greater than 5?

Given: m and n are prime numbers

Statement 1: m < 10
Let's TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 2 and n = 7. Here 3m = 6, so 3m divided by n is the same as 6 divided by 7, in which case the remainder is 6. In other words, the answer to the target question is YES, the remainder IS greater than 5
Case b: m = 3 and n = 7. Here 3m = 9, so 3m divided by n is the same as 9 divided by 7, in which case the remainder is 2. In other words, the answer to the target question is NO, the remainder is NOT greater than 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n < 6
Useful rule: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

Statement 2 tells us we are dividing by a value that is 5 is less. So, the remainder must be 4 or less
This means the answer to the target question is NO, the remainder is NOT greater than 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B