Bissoy.com
Doctors Medicines MCQs Q&A

When a positive integer n is divided by 9, the remainder is 4. What is the remainder when (3n3 + 2n2 + 5n) is divided by 9?

When a positive integer n is divided by 9, the remainder is 4. What is the remainder when (3n3 + 2n2 + 5n) is divided by 9? Correct Answer 1

Given: 

When a positive integer n is divided by 9, the remainder is 4.

Concept used:

Dividend = Divisor × Quotient + Remainder

Calculation:

According to the concept,

3n3 is divided by 9 will leave

⇒ 3 × 4 × 4 × 4

⇒ 192

⇒ when 192 is divided by 9 it leaves a remainder of 3.

2n2 is divided by 9 will leave

⇒ 2 × 4 × 4

⇒ 32

⇒ when 32 is divided by 9 it leaves a remainder of 5.

In the case of 5n,

when 5 is divided by 9 leaves a remainder of 5.

So, when 5n is divided by 9, it will leave a remainder of

⇒ 5 × 4

⇒ 20

⇒ when 20 is divided by 9 it leaves a remainder of 2.

Let the quotients be P, Q, and R respectively.

Now, when (3n3 + 2n2 + 5n) is divided by 9

⇒ (9P + 3) + (9Q + 5) + (9R + 2)

⇒ 9(P + Q + R) + 10

⇒ 9(P + Q + R + 1) + 1

⇒ Remainder of 1

∴ 1 is the remainder when (3n3 + 2n2 + 5n) is divided by 9.

Related Questions

When a certain positive integer P is divided by another positive integer, the remainder is $${r_{1}}$$ . When a second positive integer Q is divided by the same integer, the remainder is $${r_{2}}$$ and when (P + Q) is divided by the same divisor, the remainder is $${r_{3}}$$ . Then the divisor may be :
A is the smallest positive integer which when divided by 9 and 12 leaves remainder 8. B is the smallest positive integer which when divided by 9 and 12 leaves remainder 5. Which one of the following is the value of A - B?
A particular BNF definition for a “word” is given by the following rules. ∷ = | | ∷ = |  ∷ = |  ∷ = a | b | c | ….. |y| z  ∷ = 0 |1|2| …… | 9 Which of the following lexical entries can be derived from < word > ? l. pick II. picks lll. c44
Which of the positive integers below gives a remainder of 0 when it is divided by 3, if the positive integer n is divided by 3, the remainder is 1. A. n – 1 B. n + 1 C. n + 2 D. n – 3
When positive integer m is divided by positive integer n, the remainder is 6. If m/n = 112.15 what is the value of n?
When a positive integer x is divided by a positive integer y the remainder is 9. If x = 96.12 then what is the value of y ?
When a positive integer m is divided by another positive integer n. the remainder obtained is 8. If m/n=89.32, What is the value of n?
If n is an integer such that when n is divided by 2 , the remainder is 1, when n is divided by 3, the remainder is 2, and when n is divided by 4, the remainder is 3. what is the least possible value of n?
The remainder when the positive integer m is divided by 7 is x. The remainder is (x + 7) when m is divided by 14. Which one of the following could be the value of m?
When the positive integer n is divided by 18, this remainder is 7. What is the remainder when n is divided by 6?