Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Feb 2013
Posts: 836
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
04 Oct 2014, 00:51
Question Stats:
41% (02:09) correct 59% (02:06) wrong based on 227 sessions
HideShow timer Statistics
How many prime numbers exist between 200 and 220? (A) None (B) One (C) Two (D) Three (E) Four
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 03 Feb 2013
Posts: 836
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
04 Oct 2014, 00:56
BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else?



Director
Joined: 03 Feb 2013
Posts: 836
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
13 Jun 2015, 22:06
GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ? As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav The rule is if X is the number, we need to check the prime factors till \sqrt{x}



Math Expert
Joined: 02 Aug 2009
Posts: 8320

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
13 Jun 2015, 22:22
GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ?As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav hi GauravSolanky, the logic behind "the rule" of divisiblity by \(\sqrt{x}\) as also told in earlier post..... any number can be taken in various combination of multiple of two factors... However there cant be any combination which can have both factors > square root of the max square possible till that number.. in this case, 220 is between 196(14^2) and 225(15^2), so there cant be any combination which can have both factors > 14.. now 14 itself is non prime so we require to check for div for all prime no till 14, that is till13.. now if the number,202, is div by 101,a prime no but 202=101*2.. so if we have checked with 2, we dont require to check with 101.. hope the logic is clear..
_________________



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
16 Jun 2015, 00:06
GauravSolanky wrote: GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ?As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav hi GauravSolanky, the logic behind "the rule" of divisiblity by \(\sqrt{x}\) as also told in earlier post..... any number can be taken in various combination of multiple of two factors... However there cant be any combination which can have both factors > square root of the max square possible till that number.. in this case, 220 is between 196(14^2) and 225(15^2), so there cant be any combination which can have both factors > 14.. now 14 itself is non prime so we require to check for div for all prime no till 14, that is till13.. now if the number,202, is div by 101,a prime no but 202=101*2.. so if we have checked with 2, we dont require to check with 101.. hope the logic is clear.. Thanks and kudos to both of you. Regards, Gaurav The check for a Number to be prime is "If the number to be checked is NOT divisible by any prime number Less than the square root of the number then it is said to he a Prime Number" I.e. 219 will be prime if 219 is NOT divisible by any prime number less than "Square root of 219" Square root if 219 = approx.14.8 I.e. check if 219 is divisible by any one of 2,3,5,7,11,13. If 219 is not divisible by any one of these prime numbers which are less than 14.8 then 219 will be prime.
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 59725

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
04 Oct 2014, 03:47
kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? I think you did everything right.
_________________



Intern
Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
WE: Analyst (Investment Banking)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
13 Jun 2015, 21:31
kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ? As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav



Intern
Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
WE: Analyst (Investment Banking)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
14 Jun 2015, 11:53
chetan2u wrote: GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ?As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav hi GauravSolanky, the logic behind "the rule" of divisiblity by \(\sqrt{x}\) as also told in earlier post..... any number can be taken in various combination of multiple of two factors... However there cant be any combination which can have both factors > square root of the max square possible till that number.. in this case, 220 is between 196(14^2) and 225(15^2), so there cant be any combination which can have both factors > 14.. now 14 itself is non prime so we require to check for div for all prime no till 14, that is till13.. now if the number,202, is div by 101,a prime no but 202=101*2.. so if we have checked with 2, we dont require to check with 101.. hope the logic is clear.. Thanks and kudos to both of you. Regards, Gaurav



Intern
Joined: 28 Jul 2013
Posts: 9
Location: United States
Concentration: Nonprofit, Social Entrepreneurship
GMAT Date: 09012015
GPA: 3.4
WE: Information Technology (Computer Software)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
15 Jun 2015, 04:45
One more rul regarding prime no
All the prime no would be in the form of 6n +/ 1.
Cheers, Rajan



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
15 Jun 2015, 06:46
rajsinghal71 wrote: One more rul regarding prime no
All the prime no would be in the form of 6n +/ 1.
Cheers, Rajan Hi rajan, It's good that you know some properties like you mentioned here that every prime Number Greater than 3 can be represented in form of 6k+1 or 6k1 but since it's a GMAT forum so let me make it clear here that no such property is expected to be used by students in GMAT because GMAT checks very basic skills of mathematics and doesn't expect students to be loaded with various properties. P.S. Also for the reader, Please Don't use this property as Final check of a Number being Prime, however it can be a primary check to suspect if the number is prime subjected to the number satisfying this property.
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
15 Jun 2015, 23:33
GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ? As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav Check out these two posts: http://www.veritasprep.com/blog/2010/12 ... lynumber/http://www.veritasprep.com/blog/2010/12 ... tsquares/The second one ends with an explanation of this concept. Will help you understand a lot of things about factors and their placement.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
WE: Analyst (Investment Banking)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
16 Jun 2015, 12:17
VeritasPrepKarishma wrote: GauravSolanky wrote: kinjiGC wrote: BunuelI solved it using the divisibility rules. All the even numbers goes out of the window. 201,207,213,219  Sum of digits = 3 so divisible by 3 All the numbers ending with 5 is obviously not prime As 220 < 225, so maximum prime I need to check for divisibility is 13. Now rest of the numbers check one by one. 203 > Divisible by 7 209 > divisible by 11 211 > Only Prime I could get. 217 > Divisible by 7 The last step took some time. Any idea if we can use anything else? Can you please throw more light on the logic behind this ? As 220 < 225, so maximum prime I need to check for divisibility is 13.kinjiGCThanks, Gaurav Check out these two posts: http://www.veritasprep.com/blog/2010/12 ... lynumber/http://www.veritasprep.com/blog/2010/12 ... tsquares/The second one ends with an explanation of this concept. Will help you understand a lot of things about factors and their placement. Thanks Karishma, both articles were really helpful. Regards, Gaurav



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1829

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
16 Jun 2015, 12:41
GMATinsight wrote: The check for a Number to be prime is "If the number to be checked is NOT divisible by any prime number Less than the square root of the number then it is said to he a Prime Number" That should read "less than or equal to the square root". A number like 169 is not divisible by any prime less than √169, but 169 is still not a prime.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Current Student
Joined: 12 Aug 2015
Posts: 2551

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
28 Apr 2017, 19:16
Excellent Question. Here is what i did on this one >
In order to check whether a given number is prime or not => We must divide it by all the primes less than or equal to the square root of that number. PROPERTY => IF N IS NOT DIVISIBLE BY ANY PRIMES LESS THAN OR EQUAL TO THE SQAURE ROOT OF N => N is PRIMES.
Here the highest number =220 \(√220\)=> 14.something
Primes upto 14.something => {2,3,5,7,11,13}
Next => ALL PRIMES >5 MUST HAVE {1,3,7,9} as its UNITS DIGIT.
So lets check =>>
201=> Divisible by 3 => Rejected 203=>Divisible by 7 => Rejected 207=>Divisible by 3 => Rejected 209=>Divisible by 11 => Rejected 211=> Its not dividable by {2,3,5,7,11,13} => PRIME=> ACCEPTED. 213=>Divisible by 3 => Rejected 217=>Divisible by 7 => Rejected 219=>Divisible by 3 => Rejected
Hence only Prime number in the list => 211
SMASH THAT B.
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)

Re: How many prime numbers exist between 200 and 220?
[#permalink]
Show Tags
24 May 2019, 16:18
kinjiGC wrote: How many prime numbers exist between 200 and 220?
(A) None (B) One (C) Two (D) Three (E) Four 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 → So 203 is not a prime. 209/7 = 29 R 6, 209/11 = 19 → 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 → So 211 is a prime. 217/7 = 31.→ So 217 is not a prime. Therefore, there is only 1 prime number between 200 and 220. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: How many prime numbers exist between 200 and 220?
[#permalink]
24 May 2019, 16:18






