Question

How many integers are there in between 300 and 600 that are divisible by 9?

Answer 1

There are 33 integers between 300 and 600 that are divisible by 9

Given :

The integers between 300 and 600 that are divisible by 9

To find :

The number of integers between 300 and 600 that are divisible by 9

Concept :

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Solution :

Step 1 of 3 :

Write down the given numbers

The integers between 300 and 600 that are divisible by 9 are 306 , 315 , 324 , . . . . , 594

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

The arithmetic progression is

306 , 315 , 324 , . . . . , 594

First term = a = 306

Common Difference = d = 315 - 306 = 9

Step 3 of 3 :

Find the number of integers

Let number of terms in the AP = n

Then nth term of the AP = 279

a + (n - 1)d = 594

⇒ 306 + (n - 1) × 9 = 594

⇒ 306 + 9n - 9 = 594

⇒ 9n + 297 = 594

⇒ 9n = 594 - 297

⇒ 9n = 297

⇒ n = 297/9

⇒ n = 33

There are 33 integers between 300 and 600 that are divisible by 9

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Answer 2

Answer:

33 integers are there in between 300 and 600 that are divisible by 9.

Step-by-step explanation:

Short trick:

$\frac{600}{9} -\frac{300}{9}$

This values are under modulus.

$=66-33\\=33$

33 integers are there in between 300 and 600 that are divisible by 9.

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