Question

How many integers between 160 and 279 inclusive, are divisible by 7?

Answer 1

17

Explanation:

We can put this as an AP (arithmetic progression).

The first number, after 160, that is divisible by 7 is:

161

The last number before 279 that is divisible by 7 is:

273

We can use the formula:

`t_n=a+(n-1)d`

Where

tn is the nth term [here we take the last one, 273

a is the first term [161]

d is the common difference [7]

and n is the number of terms, we are trying to find this.

Substituting we get:

`t_n=a+(n-1)d\\273=161+(n-1)(7)\\273=161+7n-7\\273=154+7n\\7n=119\\n=17`

Hence, there are 17 integers