Bunuel wrote:

Official Solution:

What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35?

A. 884

B. 890

C. 892

D. 910

E. 945

# of multiples of 11 in the given range \(\frac{(\text{last}-\text{first})}{\text{multiple}}+1=\frac{(990-11)}{11}+1=90\);

# of multiples of 35 in the given range \(\frac{(\text{last}-\text{first})}{\text{multiple}}+1=\frac{(980-35)}{35}+1=28\);

# of multiples of both 11 and 35 is 2 (\(11*35=385\) and 770);

So, # of multiples of 11 or 35 in the given range is \(90+28-2=116\). Thus numbers which are not divisible by either of them is \(1000-116=884\).

Answer: A

Hi Bunuel,

I follow the approach and my answer is right too, except that my answer is not exactly right - i had to approximate

The reason= the formula i used for '# of terms between a range' is same but with different lower an upper range.

I have an understanding that:

# of terms in the range a to b (inclusive) with an even interval n = [(b-a)/n]+1

Using the same, i calculated

multiples of 11 between 1 to 1000

OR

# of terms in the range 0 to 1000 (inclusive) with an even interval 11 (as 0+11 = 11, the first no. in the range)

= [(1000-0)/11]+1 = 92 ; however the right count is 90

where is my understanding not right? TIA