Question

How many two digit numbers are there
which leaves a remainder 2 on division by 3​

Answer 1

32 digit numbers

So, there are 32 digit numbers give remainder 2 when divided by 3 or 9.

Answer 2

Answer:

The answer is $32$.

Step-by-step explanation:

To find: two digits numbers which are divisible by $3$ and leaves $2$ as a remainder.

Step 1 of 2

Since the numbers divisible by $3$ must of the form $3n$, $n\epsilon N$.

And the numbers leaves the remainder $2$ on division by $3$ will be of the form $3n+2$, $n\epsilon N$. . . . . (i)

Step 2 of 2

Finding number of $2$ digits number to hold the condition.

Consider the equation (i) as follows:

$3n+2$, $n\epsilon N$

For $n=1$, we have

⇒ $3(1)+2=5$

For $n=2$, we have

⇒ $3(2)+2=8$

For $n=3$, we have

⇒ $3(3)+2=11$

Continuing like this,

For $n=32$, we have

⇒ $3(32)+2=98$

For $n=33$, we have

⇒ $3(33)+2=101$

Notice that for $n=33$, we get three-digit. So, after $n=32$ no two-digit number exists to hold the given condition.

Therefore, there are $32$ numbers of two-digit numbers which leaves a remainder $2$ on division by $3$.

#SPJ3