What is the remainder when positive integer x is divided by 3?
1) When x is divided by 6, the remainder is 2
2) When x is divided by 15, the remainder is 2
Target question: What is the remainder when x is divided by 3?
IMPORTANT: 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
Statement 1: When x is divided by 6, the remainder is 2
This means that x = 6k + 2 (for some integer k)
Since 6 = (3)(2), we can also say that x = (3)(2)k + 2 (for some integer k)
Or we can say that, x = 3(some integer) + 2
At this point, we can see that, if we divide x by 3, the remainder must be 2.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: When x is divided by 15, the remainder is 2
We'll apply the same rule to see that x = 15k + 2 (for some integer k)
Since 15 = (3)(5), we can also say that x = (3)(5)k + 2 (for some integer k)
Or we can say that, x = 3(some integer) + 2
At this point, we can see that, if we divide x by 3, the remainder must be 2.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Remainder
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