Answer:
Remainder: 3
Step-by-step explanation:
We have been given that when positive integer k is divided by 5, the remainder is 2. We can represent this information in an equation as:
[tex]k=5n+2[/tex], where n represents quotient.
From this equation we will get possible values of k less than 40 as: {2, 7, 12, 17, 22, 27, 32, 37}
We are also told that when k is divided by 6, the remainder is 5. We can represent this information in an equation as:
[tex]k=6n+5[/tex], where n represents quotient.
From this equation we will get possible values of k less than 40 as: {5, 11, 17, 23, 29, 35}
We can see from our both sets that 17 is common number, therefore, value of k is 17.
Let us divide 17 by 7 to find our required remainder as:
[tex]\frac{17}{7}=\frac{14+3}{7}=2+\frac{3}{7}[/tex]
Therefore, the remainder would be 3, when k is divided by 7.
