Question

How many numbers amongst the numbers 9 to 99 are there which are exactly divisible by 9 but not by 3 ?

Answer 1

Answer:

All the numbers from 9 to 99 are divisible by 9 and 3

Explanation:

To know that we have to know how to divide

Answer 2

Given:

Numbers between 9 and 99

To find:

Numbers in between 9 to 99 that are divisible exactly by 9 but not divisible by 3 =?

Solution:

To find such numbers between the two given numbers we must first find out which numbers are included in the series.

Step 1: Numbers between 9 and 99 are divisible by 9 include:

=> 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Step 2: Now let us consider the divisibility rule for 9:

=> According to this if the sum of two digits is divisible by 9 the given number is exactly divisible by 9.

=> Therefore the first condition is satisfied and the numbers divisible by 9 include all the numbers mentioned above.

Step 3: To find numbers that are not divisible by 3 from the above-given numbers:

=> As we know that because the number 9 is exactly divisible by 3, therefore all those numbers which are divisible by 9 are always divisible by 3.

=> It can be deduced in the following way:

$\frac{9}{3}$ = 3

$\frac{18}{3}$ = 6

$\frac{27}{3}$ = 9

$\frac{36}{3}$ = 12

$\frac{45}{3}$ = 15

$\frac{54}{3}$ = 18

$\frac{63}{3}$ = 21

$\frac{72}{3}$ = 24

$\frac{81}{3}$ = 27

$\frac{90}{3}$= 30

$\frac{99}{3}$= 33

=> All the numbers are divisible by 3 and the second condition cannot be satisfied.

Hence, we can conclude that there are no numbers that are only divisible by 9 and not by 3 because all numbers divisible by 9 are divisible by 3 also.