HELP.....Don't understand this concept....

[smclean23]

If k and n are integers, is n divisible by 7?

1. n-3=2k
2. 2k-4 is divisible by 7.

Answer is C, both statements are sufficient......

PLEASE HELP ME!

[Ian Stewart]

If k and n are integers, is n divisible by 7?

1. n-3=2k
2. 2k-4 is divisible by 7.

Answer is C, both statements are sufficient......

PLEASE HELP ME!

This is an interesting one. I assume it's clear that neither statement is enough on its own. Let's look at both together, starting with Statement 2.

This question is partly testing whether you know that multiples of seven are seven apart: ...-14, -7, 0, 7, 14, ...

If you know, for example, that z is divisible by 7, then you can be certain that z + 7 is also divisible by 7, and that z - 7 is also divisible by 7.

From Statement 2), we know that 2k-4 is divisible by 7. Well, then (2k - 4) + 7 = 2k + 3 must also be divisible by 7. But, from Statement 1, n = 2k +3. So n must be divisible by 7.

C.