GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Nov 2018, 13:04

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# How many factors does positive integer n have?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Nov 2010
Posts: 21
How many factors does positive integer n have?  [#permalink]

### Show Tags

25 Nov 2010, 18:39
1
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:34) correct 33% (01:23) wrong based on 72 sessions

### HideShow timer Statistics

How many factors does positive integer n have?

(1) The difference between the largest and the smallest factors of n is 21

(2) n + 1 has 2 factors

M24-36

How many divisors does positive integer have?

1.The difference between the largest and the smallest divisor of is 21
2. has 2 divisors

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
S1 is sufficient. The difference between the largest and the smallest divisor of . Thus, .

S2 is not sufficient. Consider and .

The correct answer is A. Does not make sense to me at all. In order for A to be true, it looks like we have to assume all the factors are 22 consecutive integers.
Manager
Status: Still Struggling
Joined: 02 Nov 2010
Posts: 121
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

25 Nov 2010, 20:01
1
yufenshi wrote:
How many divisors does positive integer have?

1.The difference between the largest and the smallest divisor of is 21
2. has 2 divisors

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
S1 is sufficient. The difference between the largest and the smallest divisor of . Thus, .

S2 is not sufficient. Consider and .

The correct answer is A. Does not make sense to me at all. In order for A to be true, it looks like we have to assume all the factors are 22 consecutive integers.

ANS: A
I am not sure if my approach is correct, but lets c...
(A) - the smallest divisor of a number is 1 and the largest divisor of the number is the number itself. Now, as per statement A, the number seems to be 22. Hence, we can find outhow many divisors 22 has. Sufficient
(B) - As you pointed out, its not sufficient.

hence, ANS:(A)

--------------------------------------------------------------------------------------
Consider KUDOS if you like my post!
_________________

Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

Intern
Joined: 13 Nov 2010
Posts: 1
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

27 Nov 2010, 07:16
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 50627
How many factors does positive integer n have?  [#permalink]

### Show Tags

27 Nov 2010, 07:39
1
2
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many factors does positive integer n have?

(1) The difference between the largest and the smallest factors of $$n$$ is 21. The largest factor of an integer is that integer itself and the smallest factor is 1. So, we are given that $$n-1=21$$ or $$n=22$$. 22 has 4 factors: 1, 2, 11, and 22. Sufficient.

(2) $$n+1$$ has 2 factors. This statement just says that $$n+1$$ is a prime number, so $$n$$ can be for example 2 ($$2+1=3$$) and have 2 factors or 6 ($$6+1=7$$) and have 4 factors. Not sufficient.

Hope it's clear.
_________________
Manager
Joined: 07 Feb 2010
Posts: 129
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

29 Nov 2010, 06:15
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

from the statement 2 it is N has 2 divisors but you took N+1 has 2 divisors
pls explain this

Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

29 Nov 2010, 06:23
anilnandyala wrote:
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

from the statement 2 it is N has 2 divisors but you took N+1 has 2 divisors
pls explain this

I'm not sure understood your question.

Question is: what is the number of factors of N?

N+1 has 2 divisors means that N+1=prime;

Now, if N=2 then it has 2 factors (N+1=3=prime has two factors);
But if N=6 then it has 4 factors (N+1=7=prime has two factors).
_________________
Senior Manager
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

14 Nov 2017, 11:03
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

Hi Bunuel, I have a question, when considering the divisors, do we have to consider negative divisors as well.
So accordingly the least divisor will be negative of the given value and the biggest divisor will be the number itself, then statement 1 becomes $$- x + 21 = x => x = 10.5$$ but x is an integer.

Thanks
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1370
Location: India
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

14 Nov 2017, 21:52
hellosanthosh2k2 wrote:
Bunuel wrote:
vvs8787 wrote:
I don't get this one..

How many divisors does the integer has ??

A)....
B) has 2 divisors..

I thought B is the answer..

Can someone explain it even more clearly or am I missing something?

That's because yufenshi didn't post the whole question. Original question is:

How many positive divisors does positive integer N has got

(1) The difference between the largest and the smallest divisor of N is 21 --> the largest divisor of an integer is this integer itself and the smallest divisor is 1, so N-1=21 --> N=22 --> 22 has 4 factors. Sufficient.

(2) N+1 has 2 divisors --> just say that N+1 is a prime number, so N can be for example 2 (2+1=3) and have 2 factors or 6 (6+1=7) and have 4 factors. Not sufficient.

Hope it's clear.

Hi Bunuel, I have a question, when considering the divisors, do we have to consider negative divisors as well.
So accordingly the least divisor will be negative of the given value and the biggest divisor will be the number itself, then statement 1 becomes $$- x + 21 = x => x = 10.5$$ but x is an integer.

Thanks

Hi Santhoshk

As far as I know, divisors in GMAT refers ONLY to positive divisors. So for example integer '6' has only 4 divisors - which are 1, 2, 3, 6.
Manager
Joined: 10 Sep 2015
Posts: 73
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

14 Nov 2017, 22:03
please correct the question, option 2 shall be "N+1 has 2 divisors" instead of "has 2 divisors"
Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: How many factors does positive integer n have?  [#permalink]

### Show Tags

14 Nov 2017, 22:16
asthagupta wrote:
please correct the question, option 2 shall be "N+1 has 2 divisors" instead of "has 2 divisors"

Edited the question. Now, it's correct.
_________________
Re: How many factors does positive integer n have? &nbs [#permalink] 14 Nov 2017, 22:16
Display posts from previous: Sort by

# How many factors does positive integer n have?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.