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