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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## How many prime numbers exist between 200 and 220? tagged by: M7MBA ##### This topic has 2 expert replies and 1 member reply ## How many prime numbers exist between 200 and 220? How many prime numbers exist between 200 and 220? (A) None (B) One (C) Two (D) Three (E) Four The OA is B. Experts, what is the best approach that I could use to solve this PS question? May you give me some help? Legendary Member Joined 07 Sep 2017 Posted: 831 messages Followed by: 3 members Upvotes: 6 M7MBA wrote: How many prime numbers exist between 200 and 220? (A) None (B) One (C) Two (D) Three (E) Four The OA is B. Experts, what is the best approach that I could use to solve this PS question? May you give me some help? Hello M7MBA. I would solve it like this: We don't have to check the even numbers. Now, from the odd numbers: 201, 207, 210, 213, 219 are divisible by 3 (because the sum of their digits is divisible by 3). 205, 215 are divisible by 5. Hence, we have to check just the following numbers: 203, 209, 211 and 217. Now, 203 = 7*29 (NOT PRIME). 209 = 11*19 (NOT PRIME). 211 = PRIME. 217 = 7*31 (NOT PRIME). Hence the correct answer is the option B. One rule that can be useful is: if we want to know if x is a prime number, we have to divide it by all the primes between 2 and $$\sqrt{x}.$$ Since $$\sqrt{220}\approx14.8$$ then we have to check only by 2, 3, 5, 7, 11 and 13. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Vincen wrote: M7MBA wrote: How many prime numbers exist between 200 and 220? (A) None (B) One (C) Two (D) Three (E) Four The OA is B. Experts, what is the best approach that I could use to solve this PS question? May you give me some help? Hello M7MBA. I would solve it like this: We don't have to check the even numbers. Now, from the odd numbers: 201, 207, 210, 213, 219 are divisible by 3 (because the sum of their digits is divisible by 3). 205, 215 are divisible by 5. Hence, we have to check just the following numbers: 203, 209, 211 and 217. Now, 203 = 7*29 (NOT PRIME). 209 = 11*19 (NOT PRIME). 211 = PRIME. 217 = 7*31 (NOT PRIME). Hence the correct answer is the option B. One rule that can be useful is: if we want to know if x is a prime number, we have to divide it by all the primes between 2 and $$\sqrt{x}.$$ Since $$\sqrt{220}\approx14.8$$ then we have to check only by 2, 3, 5, 7, 11 and 13. Vincen has an excellent explanation here. The one thing I'll add is that if you find it difficult to see that 209 is divisible by 11, you can start with a number in the neighborhood that we know is divisible by 11, such as 220, and extrapolate. If 220 = 11*20, then 209, or 220 - 11, would contain one fewer 11. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

GMAT Instructor
Joined
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M7MBA wrote:
How many prime numbers exist between 200 and 220?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

The OA is B.

First, we can omit all the even numbers (since they are divisible by 2) and all the odd numbers ending in 5 (since they are divisible by 5). So we are left with 201, 203, 207, 209, 211, 213, 217 and 219. We can omit 201, 207, 213 and 219 also since all of these numbers are divisible by 3 (notice that the sum of their digits is divisible by 3). So we only need to consider 203, 209, 211 and 217.

203/7 = 29 â†' So 203 is not a prime.

209/7 = 29 R 6, 209/11 = 19 â†' So 209 is not a prime.

211/7 = 30 R 1, 211/11 = 19 R 2, 211/13 = 16 R 3, 211/17 = 12 R 7 â†' So 211 is a prime.

217/7 = 31.â†' So 217 is not a prime.

Therefore, there is only 1 prime number between 200 and 220.

_________________

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Founder and CEO
scott@targettestprep.com

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