Say x = 5p + 2 and y = 5q + 1; thus, x + y = 5(p + q) + 3.swerve wrote:When divided by 5, x has a remainder of 2 and y has a remainder of 1. Which of the following could be the remainder when x+y is divided by 10?
A. 6
B. 7
C. 8
D. 9
E. 0
The OA is C
Source: Manhattan Prep
Thus, (x + y)/10 = 5(p + q)/10 + 3/10
Note that when (p + q) is even, the remainder for 5(p + q)/10 is 0. Thus, the remainder for 5(p + q)/10 + 3/10 is 3. However, there is no option as 3.
Let's see what happens when (p + q) is odd. when (p + q) is odd, the units digit of 5(p + q) is 5; thus, the remainder when 5(p + q) is divide by 10 is 5.
Thus, the remainder for 5(p + q)/10 + 3/10 is 5 + 3 = 8.
The correct answer: C
Hope this helps!
-Jay
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