MathRevolution wrote:
[GMAT math practice question]
When a positive integer \(n\) is divided by \(5\), the remainder is \(2\). What is the remainder when \(n\) is divided by \(3\)?
1) \(n\) is divisible by \(2\)
2) When \(n\) is divided by \(15\), the remainder is \(2\).
Target question: What is the remainder when n is divided by 3? Given: When positive integer n is divided by 5, the remainder is 2 ----ASIDE----------------------
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 given information, we can conclude that some possible values of n are:
2, 7, 12, 17, 22, 27, 32, 37, etc Statement 1: n is divisible by 2 When we examine our list of possible n-values (
2, 7, 12, 17, 22, 27, 32, 37, ... ), we see that n could equal 2, 12, 22, 32, 42, etc
Let's test two of these possible n-values:
Case a: n = 2. In this case, 2 divided by 3 equals 0 with remainder 2. So, the answer to the target question is
the remainder is 2Case b: n = 12. In this case, 12 divided by 3 equals 4 with remainder 0. So, the answer to the target question is
the remainder is 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When n is divided by 15, the remainder is 2In other words, n is 2 greater than some multiple of 15
We can write: n = 15k + 2, where k is some integer.
IMPORTANT: notice we can take n = 15k + 2 and rewrite it as n =
3(5k) + 2
Notice that
3(5k) is a multiple of
3, which means
3(5k) +
2 is
2 MORE than some multiple of
3This means that, when we divide n by
3, the remainder is
2So, the answer to the target question is
the remainder is 2Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
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