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A positive integer n when divided by 9, gives 7 as remainder. What will be the remainder when (3n – 1) is divided by 9?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A positive integer n when divided by 9, gives 7 as remainder. What wil...
When a positive integer n is divided by 9, it gives a remainder of 7. This means that n can be written as:
n = 9k + 7
where k is a non-negative integer.
Now, we need to find the remainder when (3n + 2) is divided by 9. Substituting the value of n from the above equation, we get:
3n + 2 = 3(9k + 7) + 2
= 27k + 21 + 2
= 27k + 23
To find the remainder when (3n + 2) is divided by 9, we need to divide 27k + 23 by 9. Doing so, we get:
27k + 23 = 9(3k + 2) + 5
Therefore, the remainder when (3n + 2) is divided by 9 is 5.
n = 9k + 7
where k is a non-negative integer.
Now, we need to find the remainder when (3n + 2) is divided by 9. Substituting the value of n from the above equation, we get:
3n + 2 = 3(9k + 7) + 2
= 27k + 21 + 2
= 27k + 23
To find the remainder when (3n + 2) is divided by 9, we need to divide 27k + 23 by 9. Doing so, we get:
27k + 23 = 9(3k + 2) + 5
Therefore, the remainder when (3n + 2) is divided by 9 is 5.
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Community Answer
A positive integer n when divided by 9, gives 7 as remainder. What wil...
We have, n = 9q + 7, where q is the quotient.
⇒ 3n = 27q + 21 (Multiply by 3)
⇒ 3n – 1 = 27q + 20 = 9(3q + 2) + 2
So, remainder is 2, when (3n – 1) is divided by 9.
⇒ 3n = 27q + 21 (Multiply by 3)
⇒ 3n – 1 = 27q + 20 = 9(3q + 2) + 2
So, remainder is 2, when (3n – 1) is divided by 9.
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