Question

What is the number of integer between 300 and 400 that are exactly divisible by 7?

Answer 1

If there are n more multiples of 7 below 400, 301+7n < 400. 7n < 99. n= 13. Hence , including 301, there will be 14 integers which are multiples of 7 between 300 and 400

Answer 2

There are 15 integer between 300 and 400 that are exactly divisible by 7

Solution:

We know that,

$43 \times 7 = 301$

The first multiple of 7 after 300 is 301

$57 \times 7 = 399$

The last multiple of 7 below 400 is 399

Thus,

301 , 308 ,  ......................, 399

This forms a arithmetic progression with common difference = 7

$a_n = a_1 + (n - 1)d$

Where,

$a_n$ = last term of sequence

$a_1$ = first term of sequence

n = number of terms

d = common difference

Thus,

$399 = 301 + (n - 1) \times 7 \\\\399 - 301 = 7n - 7\\\\98 = 7n - 7\\\\7n = 105\\\\n = 15$

Thus there are 15 integer between 300 and 400 that are exactly divisible by 7

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