Problem Solving

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

Say x = 5p + 2 and y = 5q + 1; thus, x + y = 5(p + q) + 3.

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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swerve wrote: ↑

Wed Jan 08, 2020 11:54 am

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

We can let x = 2, 7, 12, 17, 22, 27, …

We can let y = 1, 6, 11, 16, 21, 26, …

If x = 7 and y = 11, we see that the remainder of 18/10 is 8.

Answer: C