An integer grater than 1 that is not prime is called : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 15:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# An integer grater than 1 that is not prime is called

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 May 2006
Posts: 227
Followers: 1

Kudos [?]: 60 [3] , given: 0

An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

25 Jun 2006, 15:05
3
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:01) correct 40% (01:04) wrong based on 535 sessions

### HideShow timer Statistics

An integer grater than 1 that is not prime is called composite. If the two-digit 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
[Reveal] Spoiler: OA

_________________

Who is John Galt?

Director
Joined: 16 Aug 2005
Posts: 945
Location: France
Followers: 1

Kudos [?]: 23 [0], given: 0

### Show Tags

25 Jun 2006, 15:27
2
This post was
BOOKMARKED
X & Y wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit 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
_________________

I believe its yogurt!

VP
Joined: 25 Nov 2004
Posts: 1493
Followers: 7

Kudos [?]: 98 [0], given: 0

### Show Tags

25 Jun 2006, 15:32
1. it could be 22, 24, 26, 28, 33 or so on.
2. it could be 21 to 29.

from 1 n is a composit. so A.
Senior Manager
Joined: 07 Jul 2005
Posts: 404
Location: Sunnyvale, CA
Followers: 2

Kudos [?]: 13 [0], given: 0

### Show Tags

25 Jun 2006, 16:21
Another one for (A)

I. 22, 26, 39 .. always composite. sufficient
II. 21-29 .. not sufficient.
Senior Manager
Joined: 11 May 2006
Posts: 258
Followers: 2

Kudos [?]: 23 [4] , given: 0

### Show Tags

25 Jun 2006, 17:14
4
KUDOS
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
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4233
Followers: 328

Kudos [?]: 3458 [2] , given: 101

Re: data sufficiency question II [#permalink]

### Show Tags

21 Dec 2009, 07:12
2
KUDOS
Expert's post
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93361 [8] , given: 10557

Re: data sufficiency question II [#permalink]

### Show Tags

21 Dec 2009, 07:53
8
KUDOS
Expert's post
4
This post was
BOOKMARKED
An integer grater than 1 that is not prime is called composite. If the two-digit 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.

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.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13681 [5] , given: 222

Re: An integer greater than 1 that is not prime is called compos [#permalink]

### Show Tags

19 Dec 2010, 15:20
5
KUDOS
Expert's post
ajit257 wrote:
Q13:
An integer greater than 1 that is not prime is called composite. If the two-digit 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.

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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 02 Nov 2012
Posts: 36
Followers: 0

Kudos [?]: 4 [0], given: 11

An integer greater than 1 that is not [#permalink]

### Show Tags

09 Jan 2013, 04:29
The tricky thing about this question was for me a very simple thing, i.e. pace. Because I was in a hurry I did not wrote down n > 20 and therefore 11 was in my range. So my advice is be calm. Because 11 is a prime where the tens digit is a factor of the units digit. This is correct isn't it?
Intern
Joined: 29 Apr 2014
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

01 Jun 2014, 19:00
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: 36590
Followers: 7092

Kudos [?]: 93361 [1] , given: 10557

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

02 Jun 2014, 00:33
1
KUDOS
Expert's post
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13489
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

03 Aug 2015, 21:22
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.
_________________
Director
Joined: 10 Mar 2013
Posts: 608
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 15

Kudos [?]: 266 [0], given: 200

An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

15 Dec 2015, 09:37
X & Y wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit 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

The most important point is here that means that tens digit is > 1 (because 1 is a factor of any number, and it would make the whole calculation here too complex)
1 is a divisor of every integer. And zero is a multiple of every integer, including zero.

(1) If a units digit has a factor other than 1 and itself it's not prime, consider also these numbers 33, 44, 55 etc which have 11 as a factor- $$SUFFICIENT$$
(2) We already know that. Clearly not sufficient
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Senior Manager
Joined: 17 Jun 2015
Posts: 270
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT 3: Q V
Followers: 3

Kudos [?]: 20 [0], given: 165

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

20 Dec 2015, 04:06
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

Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4233
Followers: 328

Kudos [?]: 3458 [0], given: 101

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

20 Dec 2015, 04:20
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Senior Manager
Joined: 17 Jun 2015
Posts: 270
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT 3: Q V
Followers: 3

Kudos [?]: 20 [0], given: 165

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

20 Dec 2015, 04:23
chetan2u wrote:
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

Thanks a lot. Much appreciated. Was figuring out ways to remember certain tricks. Thanks again for the correction
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Intern
Joined: 18 Sep 2013
Posts: 5
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 0 [0], given: 163

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

27 Jul 2016, 01:25
Bunuel wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit 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.

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 ,

it is a prime number and
7 is factor of 1.
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93361 [1] , given: 10557

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

27 Jul 2016, 02:32
1
KUDOS
Expert's post
munishrattanpal wrote:
Bunuel wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit 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.

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 ,

it is a prime number and
7 is factor of 1.

7 is not a factor of 1, 7 is a multiple of 1.
_________________
Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 294
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
Followers: 18

Kudos [?]: 233 [0], given: 260

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

27 Jul 2016, 03:38
Top Contributor
munishrattanpal wrote:
Bunuel wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit 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.

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 ,

it is a prime number and
7 is factor of 1.

1 is a factor of 7 but not other way around.
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Senior Manager
Joined: 02 Mar 2012
Posts: 374
Schools: Schulich '16
Followers: 4

Kudos [?]: 63 [0], given: 4

Re: An integer grater than 1 that is not prime is called [#permalink]

### Show Tags

28 Jul 2016, 00:54
good question

1)tens digit is a factor of unit digit and GIVEN-n>20

only 2,3,4 and 5 suffice

so number with 2 would be

26=2 & 6(2*3) always a multiple of 2 or 2 as common.so more than 2 factors.Composite
Similar for other nos

36 or 33=3 & 6 or 3 & 3

so A is suff

2)tens digit is 2

can be 23 or 26(prime or comp)

insuff

Ans- A
Re: An integer grater than 1 that is not prime is called   [#permalink] 28 Jul 2016, 00:54

Go to page    1   2    Next  [ 27 posts ]

Similar topics Replies Last post
Similar
Topics:
1 Is integer r prime? (1) r + 1 is prime (2) r is greater than 10 5 10 Dec 2016, 05:36
1 If p is an integer greater than 1, is p a prime number? 1 21 Dec 2015, 15:00
23 The Prime Sum of an integer X greater than 1 is the sum of all prime 13 09 Apr 2015, 03:52
18 If x is a positive integer greater than 1, is x a prime numb 17 14 Feb 2014, 01:13
24 An integer greater than 1 that is not prime is called 9 08 Jan 2008, 05:20
Display posts from previous: Sort by