Question

7 Find how many two digit numbers are divisible by 6 ?​

Answer 1

Answer:

15

Complete step by step answer:

As we know that the two digit number is from (10 to 99).

So the first two digit number which is divisible by 6 is 12, second two digit number which is divisible by 6 is (12 + 6 = 18) and the last two digit number which is divisible by 6 is 96.

So the sequence of two digit numbers which is divisible by 6 is

12, 18, 24, .................. 96.

Now as we see this follows the trend of an arithmetic progression (A.P) whose first term (a1) = 12, common difference (d) = (18 – 12) = (24 – 18) = 6 and the last term (an) = 96.

Now as we know that the last term or nth term of an A.P is calculated as

⇒an=a1+(n−1)d⇒an=a1+(n−1)d where symbols have their usual meanings and n is the number of terms.

So substitute all the values in this equation we have,

⇒96=12+(n−1)6⇒96=12+(n−1)6

Now simplify the above equation we have,

⇒96−12=(n−1)6⇒96−12=(n−1)6

⇒6(n−1)=84⇒6(n−1)=84

Now divide by 6 we have

⇒n=846+1⇒n=846+1

⇒n=14+1=15⇒n=14+1=15

So the number of two digit numbers which are divisible by 6 are 15.

So this is the required answer.

So the number of two digit numbers which are divisible by 6 are 15.

Step-by-step explanation:

please mark me brilliant ❤️