BTGModeratorVI wrote: ↑

Sat Mar 28, 2020 9:54 am

When a positive integer n is divided by 7, what is the remainder?
1) When n - 294 is divided by 7, the remainder is 3
2) n - 3 is divisible by 7

Answer: D
Source: Math Revolution

Target question: What is the remainder when positive integer n is divided by 7?

Statement 1: When n-294 is divided by 7, the remainder is 3
ASIDE: There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2

The statement tells us that when n - 294 is divided by 7, the remainder is 3
So, using the above rule, we can say that: n - 294 = 7k + 3, for some integer k.
Take n - 294 = 7k + 3 and...
...add 294 to both sides to get: n = 7k + 294 + 3 [you'll see why I wrote the right side this way]
Since 294 = (7)(42), we can write: n = 7(k + 42) + 3
This tells us that n is 3 GREATER THAN some multiple of 7.
So, if we divide n by 7, the remainder will be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n-3 is divisible by 7
In other words, n-3 = 7j for some integer j.
If we add 3 to both sides we get: n = 7j + 3
This tells us that n is 3 GREATER THAN some multiple of 7.
So, if we divide n by 7, the remainder will be 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D