**Quote:**

I understand how you got *n* = 5*k* + 4

We get

*n* = 5

*k* +

3 from the question statement, because the remainder is 3.

**Quote:**

Where exactly did (5*k* + 7)² come from?

We plug

*n* = 5

*k* +

3 into (

*n* + 4)² and get

(

*n* + 4)² = (5

*k* + 3 + 4)²

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Furthermore, I'd like to bring your attention to 2 important moments here:

1. Representation like

*n* = 5

*k* + 3 is a very good simple method based on the definition of the division with a remainder.

2. In GMAT we can substitute the remainder itself, e.g. 3, instead general representation (

*n* = 5

*k* +

3), IF the assumption that the remainder must be the same for ANY

*n* is TRUE (which can be easily see from the statement).