Max@Math Revolution wrote:
When a positive integer n is divided by 3, what is the remainder?
1) When n is divided by 5, the remainder is 2
2) When n is divided by 6, the remainder is 2
Target question: What is the remainder when positive integer n is divided by 3?
Statement 1: When n is divided by 5, the remainder is 2
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When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
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So, from the information in statement 1, some possible values of n are: 2, 7, 12, 17, 22, 27, ...
Let's TEST a couple of values:
Case a: If n = 2, then the answer to the target question is
the remainder is 2 when n is divided by 3
Case b: If n = 7, then the answer to the target question is
the remainder is 1 when n is divided by 3
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When n is divided by 6, the remainder is 2
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There's a nice rule that says, "
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
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Let's take statement 2 and rewrite it as follows: When n is divided by 6, the quotient is k and the remainder is 2
From the above rule, we can write: n = 6k + 2
We can rewrite the right side as: n =
3(2k) + 2
We can see that
3(2k) is a multiple of
3
This means
3(2k) + 2 is
2 greater than a multiple of 3
So, when we divide
3(2k) + 2 by 3 the remainder must be 2
This means the answer to the target question is
the remainder is 2 when n is divided by 3
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
