We have to determine the value of the remainder when (n - 3)^2 is divided by 4.Vincen wrote:If n is an integer, what is the remainder when (n - 3)^2 is divided by 4?
(1) n is divisible by 2.
(2) n is divisible by 4.
OA is D.
How can I solve this exercise? Is it a fast way to do it?
Statement 1: n is divisible by 2.
Say n = 2k; where k is an integer
Thus, (n - 3)^2 = (2k - 3)^2 = 4k^2 - 12k + 9
So, we have to determine the remainder when 4k^2 - 12k + 9 is divided by 4.
We see that 4k^2 is divisible by 4, leaving a remainder of 0; similarly, -12k is divisible by 4, leaving a remainder of 0; 9 is divisible by 4 leaves a remainder of 1.
Thus, the remainder = 1. Sufficient.
Sufficient.
Statement 2: n is divisible by 4.
Say n = 4k; where k is an integer
Thus, (n - 3)^2 = (4k - 3)^2 = 16k^2 - 24k + 9
With the same analysis as done in (1), we get the remainder = 1. Sufficient.
The correct answer: D
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Jakarta | Nanjing | Berlin | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
