Max@Math Revolution 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
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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 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 2
Case 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 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When n is divided by 15, the remainder is 2
In 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
3
This means that, when we divide n by
3, the remainder is
2
So, the answer to the target question is
the remainder is 2
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
