NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 01:18 It is currently 25 Apr 2024, 01:18
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

An integer greater than 1 that is not prime is called composite.

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
XxxyyY
Manager
Manager
Joined: 25 May 2006
Posts: 113
Own Kudos [?]: 323 [207]
Given Kudos: 0
Send PM
An integer greater than 1 that is not prime is called composite. [#permalink] New post   25 Jun 2006, 16:05
19
Kudos
188
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

68% (01:46) correct 32% (01:43) wrong based on 2368 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [68]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   21 Dec 2009, 08:53
26
Kudos
42
Bookmarks
Expert Reply
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.

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.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14822
Own Kudos [?]: 64907 [30]
Given Kudos: 426
Location: Pune, India
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   19 Dec 2010, 16:20
23
Kudos
7
Bookmarks
Expert Reply
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.

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).
User avatar
gmatmba
Director
Director
Joined: 16 Aug 2005
Posts: 518
Own Kudos [?]: 112 [22]
Given Kudos: 0
Location: France
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   25 Jun 2006, 16:27
11
Kudos
11
Bookmarks
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
General Discussion
User avatar
iced_tea
Manager
Manager
Joined: 11 May 2006
Posts: 146
Own Kudos [?]: 392 [14]
Given Kudos: 0
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   25 Jun 2006, 18:14
8
Kudos
5
Bookmarks
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
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11172
Own Kudos [?]: 31898 [4]
Given Kudos: 290
Send PM
Reviews Badge
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   21 Dec 2009, 08:12
4
Kudos
Expert Reply
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
avatar
mrvora
Intern
Intern
Joined: 30 Apr 2014
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [3]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   02 Jun 2014, 01:33
3
Kudos
Expert Reply
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.
avatar
munishrattanpal
Intern
Intern
Joined: 18 Sep 2013
Posts: 4
Own Kudos [?]: 6 [0]
Given Kudos: 163
Schools: AGSM '18 Melbourne '19
WE:Engineering (Manufacturing)
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   27 Jul 2016, 02:25
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.

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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [1]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   27 Jul 2016, 03:32
1
Kudos
Expert Reply
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.

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.
avatar
B
20043856
Intern
Intern
Joined: 27 Oct 2015
Posts: 3
Own Kudos [?]: 12 [0]
Given Kudos: 6
Send PM
GMAT ToolKit User
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   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?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   06 Jan 2017, 06:16
Expert Reply
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.
User avatar
G
anairamitch1804
Director
Director
Joined: 26 Oct 2016
Posts: 510
Own Kudos [?]: 3379 [2]
Given Kudos: 877
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   29 Jan 2017, 18:21
1
Kudos
1
Bookmarks
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 .
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 966
Own Kudos [?]: 223 [1]
Given Kudos: 434
Location: United States
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   05 Nov 2020, 03:34
1
Kudos
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.

Lets try to find a prime number that would work in this scenario. Since the number has to be greater than 20, we can't use 11, 13, etc.

33 is a composite number, as is 77. SUFFICIENT.

(2) The tens digit of n is 2

We can get a prime number and a composite number. 23 is prime, 21 is composite. INSUFFICIENT.

Answer is A.
User avatar
B
smmc29
Intern
Intern
Joined: 27 Sep 2020
Posts: 43
Own Kudos [?]: 7 [1]
Given Kudos: 246
Location: Philippines
Concentration: General Management, Nonprofit
Schools: Stanford '23 (S)
GMAT 1: 700 Q49 V35 (Online)
GPA: 3.4
WE:Consulting (Consulting)
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   25 Feb 2021, 09:29
1
Kudos
(1) n = ab

n = 10a + b

If a is a factor of b then ax = b

n = a(10+x) we can see here immediately that since we can factor out a then a will serve as another factor of n. Also a cannot be equal to 1 as stated in the question stem. Thus n is composite.

SUFFICIENT.

(2) clearly insufficient (23,29)

Answer is A.
User avatar
D
mcelroytutoring
Tutor
Joined: 10 Jul 2015
Status:Expert GMAT, GRE, and LSAT Tutor / Coach
Affiliations: Harvard University, A.B. with honors in Government, 2002
Posts: 1178
Own Kudos [?]: 2412 [0]
Given Kudos: 272
Location: United States (CO)
Age: 44
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169

GRE 2: Q170 V170
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   05 Jun 2022, 15:07
Expert Reply
Top Contributor
This question makes a good argument for memorizing all the primes less than 100.

If you know all the two-digit primes in advance, then you can simply rule them out individually.

What do the numbers 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 all have in common? The tens digit (the first digit) is not divisible by the ones digit.
User avatar
B
ayushituteja02
Intern
Intern
Joined: 29 Mar 2023
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 3
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   29 Mar 2023, 04:42
but this question talks about a single "integer" and if the statements are not boiling down to a single correct answer- isn't it still incomplete?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618875 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   29 Mar 2023, 07:45
Expert Reply
ayushituteja02 wrote:
but this question talks about a single "integer" and if the statements are not boiling down to a single correct answer- isn't it still incomplete?


There are two types of data sufficiency questions:

1. YES/NO DS Questions:

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".


2. VALUE DS QUESTIONS:

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

This question belongs to the first type. Notice that the question asks "is is n composite?" not "what is the value of n" and from the first statement we can get a definite YES answer to the question.

Hope it's clear.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32662
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: An integer greater than 1 that is not prime is called composite. [#permalink] New post   30 Mar 2024, 22:42
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.
GMAT Club Bot
gmatclubot
Re: An integer greater than 1 that is not prime is called composite. [#permalink]
30 Mar 2024, 22:42
Moderator:
Bunuel
Math Expert
92901 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions