BTGModeratorVI wrote: ↑Tue Feb 18, 2020 11:06 am
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?
A. 1
B. 3
C. 5
D. 7
E. 9
Answer:
C
Source: Magoosh
Solution:
Since x + 2 is divisible by 10, then x + 2 could equal 10, and hence, x could equal 8. (Note, that x + 2 could also equal 20, or 30, or any positive multiple of 10).
We’ll choose x = 8, and we have:
8^2 + 4(8) + 9 = 64 + 32 + 9 = 105
Since 105/10 = 10 R 5, the remainder is 5.
Alternate Solution:
Let’s write x^2 + 4x + 9 = x^2 + 4x + 4 + 5 = (x + 2)^2 + 5.
Since x + 2 is divisible by 10, (x + 2)^2 is also divisible by 10. Hence, the remainder when x^2 + 4x + 9 = (x + 2)^2 + 5 is divided by 10 is 5.
Answer: C
