What is the Number of Integers from 1 to 1000, Inclusive that are not Divisible by 11 or by 35? GMAT Problem Solving

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

1. 884
2. 890
3. 892
4. 910
5. 945

“What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach Solution 1

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

# of the multiples of 11 in the given range: \(\frac{(last-first)}{multiple}+1\) = \(\frac{(980-35)}{35}+1\) = 28;

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

So, # of the multiples of both 11 and 35 in the given range is 90 + 28 – 2 = 116

Thus the numbers which are not divisible by either of them is 1000 – 116 = 884

Correct option: A

Approach Solution 2

\(\frac{1000}{11}=90\), xx so we have 90 multiples of 11 in 1000

\(\frac{1000}{35}=28\), xx so we have 28 multiples of 35 in 1000

Now, because we counted a few multiples of both 11 and 35 we need subtract them:

\(\frac{1000}{(35*11)}=2\), xx so we need to subtract 2 multiples of both 11 and 35

Altogether;
90 + 28 – 2 = 116
So, we have 1000 – 116 = 884 integers that are NOT divisible by 11 or 35

Correct option: A

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