What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?

* 884

* 890

* 892

* 910

* 945

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We can go this way:

Calculate the no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both.

1.) Total no. of terms divisible by 11 are

90. We can calculate this by finding the first and last terms, which are 11 & 990 respectively. Then we will find the total no. of terms by using equation

Last Term = a + (n-1)d where a=11, d=11, Last Term=990.

So, n=90

2.) Similarly, total no. of terms divisible by 35 are

28. Find it using the above method.

3.) To find terms divisible by both 11 & 35, find the first term. Since both have no common factors except 1, just multiply 11 & 35 to get the first common term i.e., 385. Next term is 770.

So, in total, there are

2 common terms for 11 & 35.

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Hence, the total no. of terms from 1 to 1000 (inclusive) that are divisible by 11 or 35 or both = 90 + 28 - 2 = 116

So, the correct answer = 1000 - 116 =

884, which will give us the total no. of terms that are divisible neither by 11 nor 35.

So, I'll go for first option, i.e.,

884Though the explanation looks a bit lengthy, it'll not take much time to solve.

HTH

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+++ Believe me, it doesn't take much of an effort to underline SC questions. Just try it out. +++

+++ Please tell me why other options are wrong. +++

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