Data Sufficiency

ardz24 wrote:When n is divided by 5, what is the remainder?

1) When n is divided by 3, the remainder is 2
2) When n+1 is divided by 5, the remainder is 3

Target question: When n is divided by 5, what is the remainder?

Statement 1: When n is divided by 3, the remainder is 2
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.

So, if n divided by 3 yields a remainder of 2, some possible values of n are: 2, 5, 8, 11, 14, 17, etc
Let's test two possible values of n
Case a: n = 2. In this case, n divided by 5 yields are remainder of 2
Case b: n = 5. In this case, n divided by 5 yields are remainder of 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n+1 is divided by 5, the remainder is 3
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

Given: When n+1 is divided by 5, the remainder is 3
We're not told the quotient (Q), so let's say the quotient is some integer k
We can say "When n+1 is divided by 5, the quotient is k and the remainder is 3"
So, we can say that n+1 = 5k + 3
Subtract 1 from both sides to get: n = 5k + 2
5k is a multiple of 5, so 5k+2 is 2 greater than some multiple of 5
So, if we divide 5k+2 by 5, the remainder will be 2.
In other words, n divided by 5 yields are remainder of 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent