Q12. - Algebra 2

Question

The integer k is greater than 50 and less than 100. When k is divided by 3, the remainder is 1. When k is divided by 8, the remainder is 2. What is one possible value of k?

Step-by-Step Solution

Answer

The one possible value of $k$ is 82.

Step 1 – Describe the given data.

Suppose k is a number that lies between 50 and 100.

 

Here, when k is divided by 3, the remainder is 1, and when k is divided by 8, the remainder is 2.

Step 2 – Find the multiples of 3 and 8 which are lies between 50 and 100.

The multiples of 3 that are lies between 50 and 100 are as follows:

 

$51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99$.

 

The multiples of 8 that are lies between 50 and 100 are as follows:

 

$56,64,72,80,88,96$.

Step 3 – Find number.

By observing the multiples, notice that if we divide the number 82 by 3, the remainder is 1, and when the number 82 by 8, the remainder is 2.

 

Hence, the one possible value of k is 82.