BTGModeratorVI wrote: ↑Sat Mar 28, 2020 9:58 am
When a positive integer m^2 is divided by 4, what is the remainder?
1) When m is divided by 3, the remainder is 1
2) When m is divided by 2, the remainder is 1
Answer:
B
Source: Math Revolution
Target question: What is the remainder when m² is divided by 4?
Statement 1: When m is divided by 3, the remainder is 1
Let's TEST some values.
There are several values of m that satisfy statement 1. Here are two:
Case a: m = 4, which means m² =16. In this case,
the remainder is 0 when m² is divided by 4
Case b: m = 7, which means m² =49. In this case,
the remainder is 1 when m² is divided by 4
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When m is divided by 2, the remainder is 1
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
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
So, in this case, we can write: m = 2k + 1 (where k is some integer)
If m = 2k + 1, then m² = (2k + 1)² = 4k² + 4k + 1 = 4(
k² + k) + 1
In other words, m² = 4(
some integer) + 1
Since m² is
1 GREATER THAN some multiple of 4, we can conclude that
the remainder is 1 when m² is divided by 4
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
