When positive integer k is divided by 5, the remainder is 2. when k is divided by 6, the remainder is 5. if k is less than 40, what is the remainder when k is divided by 7?

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:

, 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:

, 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:

Therefore, the remainder would be 3, when k is divided by 7.

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step-by-step explanation:

2 tens + 6 ones

1 ten + 16 ones

0 tens + 26 ones