Zarrolou
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
We should recall that when dividing by 5, we only need to know the units digit of the divisor to determine the remainder. Thus, when x is divided by 5 and the remainder is 2, the units digit of x must be either 7 or 2. Also, when y is divided by 5 and the remainder is 1, the units digit of y must be either 6 or 1.
Likewise, when dividing by 10, we only need to know the units digit of the divisor to determine the remainder. Let’s now determine some possible sums of x and y.
x + y = 7 + 6 = 13, which has a remainder of 3 when divided by 10.
x + y = 7 + 1 = 8, which has a remainder of 8 when divided by 10.
x + y = 2 + 6 = 8, which has a remainder of 8 when divided by 10.
x + y = 2 + 1 = 3, which has a remainder of 3 when divided by 10.
Thus, the possible remainders when x + y is divided by 10 are 3 and 8. Since only 8 is given in the answer choices, the correct answer is C.
Answer: C