saintforlife wrote:What is the remainder when the positive integer g is divided by 7?
1. When g is divided by 14, the remainder is 8
2. g is the sum of two distinct positive integers
Target question: What is the remainder when g is divided by 7?[/color]
Statement 1: When g is divided by 14, the remainder is 8
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
In this statement, we're told that g divided by 14 equals some unknown value (say k) with remainder 8.
From this, we know that g = 14k + 8 for some integer k.
We can now rewrite this as g = (7)(2)(k) + 8
Or g = (7)(2)(k) + 7 + 1
Now we'll factor the 7 out of the first part to get: g = 7[2k + 1] + 1
This tells us that,
when g is divided by 7, the remainder must be 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: g is the sum of two distinct positive integers
There are several values of g that meet this condition. Here are two:
Case a: g = 2+5 = 7, in which case
g divided by 7 leaves remainder 0
Case b: g = 2+6 = 8, in which case
g divided by 7 leaves remainder 1
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
