Question

Find the number of integers between $100$ & $1000$ that are not divisible by $7$.

• A. $552$
• B. $646$
• C. $704$
• D. $772$

Answer 1

Answer: (D)

$772$

Numbers between $100$ and $1000$ which are exactly divisible by $7$.

$\Rightarrow \frac{100}{7}=14.28<15$

$\Rightarrow \frac{1000}{7}=142.85>142$

Hence, the numbers which are exactly divisible by $7$ are:

1st number $=7\times 15=105$

2nd $=7\times 16=112$

3rd $=7\times 17=119$ and so on till $142\times 7=994$

Also, $142-14=128$

There are total $128$ numbers which are exactly divisible by $7$ between $100$ and $1000$.

Total integers between $100$ and $1000$ is $1000-100=900$

So, number of integers not divisible by $7$ is $=900-128=772$