Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted. Aug 31 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Sep 01 07:00 AM PDT  09:00 AM PDT Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT Sep 02 08:00 PM PDT  11:00 PM PDT Sign Up, Get $49 Exam Pack 2 FREE. Train to be ready for Round 1 Deadlines with EMPOWERgmat's Score Booster Code: EP22019 Ends: September 2nd
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 May 2006
Posts: 205

An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
25 Jun 2006, 16:05
Question Stats:
65% (01:37) correct 35% (01:44) wrong based on 719 sessions
HideShow timer Statistics
An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite? (1) The tens digit of n is a factor of the units digit of n. (2) The tens digit of n is 2
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 57255

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
21 Dec 2009, 08:53
An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?Given: \(n>20\) > two digit integer can be written as follows: \(n=10b+a>20\) > \(2\leq{b}\leq{9}\), \(0\leq{a}\leq{9}\). (1) The tens digit of n is a factor of the units digit of n. This statement implies that \(a=kb\), (\(0\leq{k}\leq{4}\)) > \(n=10b+a=10b+kb=b(10+k)\) > as \(b\geq{2}\), \(n\) will always be composite and factor of \(b\). Sufficient (2) The tens digit of n is 2. This statement implies that \(b=2\), but \(n\) can be for instance composite 25 or prime 29. Not sufficient. Answer: A. chetan2u wrote: A.. SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite.... SII.. no can be any of 21,22,23.....29..ie mix of composite and prime Actually units digit of \(n\) can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99.
_________________




Manager
Joined: 11 May 2006
Posts: 225

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
25 Jun 2006, 18:14
me too A.
considering A, the number can be written as
a(ak)
where a is the tens digit and ak is the unit digit, k is some constant.
= 10a + ak
= a(10+k)
this is always divisible by a and hence composite since a is not equal to 1




Director
Joined: 16 Aug 2005
Posts: 830
Location: France

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
25 Jun 2006, 16:27
X & Y wrote: An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?
(1) The tens digit of n is a factor of the units digit of n.
(2) The tens digit of n is 2
Plz Explain..
(1) 24 (2 is a factor of 4), 39 (3 is a factor of 9), 48 (4 is a factor of 8) ... sufficient
(2) 22 composite, 23 not composite  not sufficient
_________________



Math Expert
Joined: 02 Aug 2009
Posts: 7754

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
21 Dec 2009, 08:12
A.. SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite.... SII.. no can be any of 21,22,23.....29..ie mix of composite and prime
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9561
Location: Pune, India

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
19 Dec 2010, 16:20
ajit257 wrote: Q13: An integer greater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?
(1) The tens digit of n is a factor of the units digit of n. (2) The tens digit of n is 2.
Not sure about the ans The moment I hear two digit prime number, I think of numbers having 1/3/7/9 as unit's digit. A two digit number ending in 0/2/4/5/6/8 cannot be prime since they are either even or a multiple of 5 (if it is a single digit, 5 is prime) Stmnt 1: Ten's digit is a factor of the unit's digit. It is easy to see that there are many such composite numbers e.g. 24, 26 etc. I will try to find if there are any such prime numbers: The only factor of 1 is 1; of 3 are 1 and 3; of 7 are 1 and 7; of 9 are 1, 3 and 9. 11, 13, 17 and 19 are not allowed since the number should be greater than 20. 33, 77, 39 and 99 are all composite. So there is no such prime number. All such number will be composite so n is composite. Hence sufficient. Stmnt 2: The tens digit of n is 2. 21 is not prime while 23 is. Hence not sufficient. Answer (A).
_________________
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: 30 Apr 2014
Posts: 3

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
01 Jun 2014, 20:00
Hi Bunuel,
I got the answer by other way. However, i would like to understand your explanation on (1) where you stated that a=kb, (0<=k<=4) > n=10b+a=10b+kb=b(10+k) > as b>=2, n will always be composite and factor of b.
Can you please explain in detail this a=kb part? why (0<=k<=4)?
Regards, Mitesh



Math Expert
Joined: 02 Sep 2009
Posts: 57255

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
02 Jun 2014, 01:33
mrvora wrote: Hi Bunuel,
I got the answer by other way. However, i would like to understand your explanation on (1) where you stated that a=kb, (0<=k<=4) > n=10b+a=10b+kb=b(10+k) > as b>=2, n will always be composite and factor of b.
Can you please explain in detail this a=kb part? why (0<=k<=4)?
Regards, Mitesh (1) says that the tens digit of n, which is b, is a factor of the units digit of n, which is a. So, b is a factor of a > \(a=kb\), for some integer k. As for \(0\leq{k}\leq{4}\): the least value of b is 2, thus if k is 5 or more, then a becomes 10 or more, which is not possible since we know that a is a digit (\(0\leq{k}\leq{4}\)). Hope it's clear.
_________________



Manager
Joined: 17 Jun 2015
Posts: 198
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
20 Dec 2015, 05:06
A two digit number comprised of two composite numbers is always composite. (1) is sufficient. B is not sufficient. With thens digit as 2, the number could be 29, which is prime and 24, which is composite.
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Math Expert
Joined: 02 Aug 2009
Posts: 7754

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
20 Dec 2015, 05:20
hdwnkr wrote: A two digit number comprised of two composite numbers is always composite. (1) is sufficient.
B is not sufficient. With thens digit as 2, the number could be 29, which is prime and 24, which is composite. Hi, the statement may not be correct... 89 is a prime number, which has both digits composite.. stat 1 is suff but not for the reason you have mentioned.. there is no prime number till 100 satisfying the condition of 1
_________________



Intern
Joined: 18 Sep 2013
Posts: 5
WE: Engineering (Manufacturing)

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
27 Jul 2016, 02:25
Bunuel wrote: An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?Given: \(n>20\) > two digit integer can be written as follows: \(n=10b+a>20\) > \(2\leq{b}\leq{9}\), \(0\leq{a}\leq{9}\). (1) The tens digit of n is a factor of the units digit of n. This statement implies that \(a=kb\), (\(0\leq{k}\leq{4}\)) > \(n=10b+a=10b+kb=b(10+k)\) > as \(b\geq{2}\), \(n\) will always be composite and factor of \(b\). Sufficient (2) The tens digit of n is 2. This statement implies that \(b=2\), but \(n\) can be for instance composite 25 or prime 29. Not sufficient. Answer: A. chetan2u wrote: A.. SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite.... SII.. no can be any of 21,22,23.....29..ie mix of composite and prime Actually units digit of \(n\) can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99. Hi , What about No. 71 . it is a prime number and 7 is factor of 1.



Math Expert
Joined: 02 Sep 2009
Posts: 57255

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
27 Jul 2016, 03:32
munishrattanpal wrote: Bunuel wrote: An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?Given: \(n>20\) > two digit integer can be written as follows: \(n=10b+a>20\) > \(2\leq{b}\leq{9}\), \(0\leq{a}\leq{9}\). (1) The tens digit of n is a factor of the units digit of n. This statement implies that \(a=kb\), (\(0\leq{k}\leq{4}\)) > \(n=10b+a=10b+kb=b(10+k)\) > as \(b\geq{2}\), \(n\) will always be composite and factor of \(b\). Sufficient (2) The tens digit of n is 2. This statement implies that \(b=2\), but \(n\) can be for instance composite 25 or prime 29. Not sufficient. Answer: A. chetan2u wrote: A.. SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite.... SII.. no can be any of 21,22,23.....29..ie mix of composite and prime Actually units digit of \(n\) can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99. Hi , What about No. 71 . it is a prime number and 7 is factor of 1. 7 is not a factor of 1, 7 is a multiple of 1.
_________________



Intern
Joined: 27 Oct 2015
Posts: 5

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
06 Jan 2017, 05:52
Please explain, why can't we consider 31( or 41) number for statement 1.
Is 3 a factor of 1?



Math Expert
Joined: 02 Sep 2009
Posts: 57255

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
06 Jan 2017, 06:16
20043856 wrote: Please explain, why can't we consider 31( or 41) number for statement 1.
Is 3 a factor of 1? In 31, 3 is the tens digit and 1 is the units digit. (1) says that the tens digit of n is a factor of the units digit of n but 3 is NOT a factor of 1, 1 is a factor of 3, or in another way 3 is a multiple of 1. Hope it's clear.
_________________



Director
Joined: 26 Oct 2016
Posts: 624
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
29 Jan 2017, 18:21
For condition one  They have mentioned that ten's digit is a factor of one's digit. Implying that numbers are  22 ( 2 is factor of 2 ) , 24 ( 2 is a factor of 4 ) , 26, 28, 33, 36, 39 etc. Thus these numbers are composite as they are not prime. Condition 2 , gives us 21,22,23,24....29. Of which 23, 29 are prime . Thus insufficient. IMO  A .
_________________
Thanks & Regards, Anaira Mitch



Manager
Joined: 31 Dec 2016
Posts: 68

Re: An integer grater than 1 that is not prime is called composite. If the
[#permalink]
Show Tags
30 Jul 2017, 12:46
gmatmba wrote: X & Y wrote: An integer grater than 1 that is not prime is called composite. If the twodigit integer n is greater than 20, is n composite?
(1) The tens digit of n is a factor of the units digit of n.
(2) The tens digit of n is 2
Plz Explain.. (1) 24 (2 is a factor of 4), 39 (3 is a factor of 9), 48 (4 is a factor of 8) ... sufficient (2) 22 composite, 23 not composite  not sufficient This isn't a good way to do it because really you should be looking at primes and not composites. If one prime had a factor where the tens digit was a factor of its units then your answer is destroyed. All you did was prove that composites have some tens digits which are factors of units digitsit is impossible above 5 really for the tens to be a factor of the units because 6 doesn't go into 1,2,3,4,5,7,8,9. And we know 66,77,88 and 99 aren't prime as they have factors of 11 . (1) It's better to list the prime. The prime between 2060you should memorize. Are: 23,29,31,37,41,43,49,53,59 and 61. Notice how none of the Tens are factors of the units number. So we know for a prime that the tens digit is not a factor of the units digit. For a composite we can have one example 22, in which we see the tens is a factor of the units. (2 is a factor of 2). So we can see primes don't have tens that are factors of units between 20100 and composites can. Therefore it is not a prime and therefore is a composite(2) If the 10's digit is 2, the number could be 22 or 23. NS Answer is therefore A



NonHuman User
Joined: 09 Sep 2013
Posts: 12092

Re: Number Property
[#permalink]
Show Tags
11 Jun 2019, 05:34
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: Number Property
[#permalink]
11 Jun 2019, 05:34






