Hi All,
With a bit of logic, and using the answer choices as reference, you can answer this question without having to do ANY calculations.
We're told that two points are on the opposite sides of a square whose sides are 4. We're asked which of the following COULD be the distance between these two points.
Since we don't know exactly where the two points are, we should start with what would be the SHORTEST distance between them, then we can work 'up' from there.
If the points were at the exact some 'place' on opposite sides, then they would be the same distance as the length of a side: 4. That length is the SHORTEST distance between possible points, so Answer A is impossible. As we slide either (or both) points along the sides of the square, the distance will become GREATER than 4. So we could move one (or both) of the points so that they were 4.1 apart (or 4.2 or 4.325, etc.). Logically, the answer CANNOT be 6, because if 6 were a possibility, then 5 would ALSO be a possibility. Since there's only one correct answer to this question, it MUST be the smallest number that is greater than 4...
Final Answer:
GMAT assassins aren't born, they're made,
Rich