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

It is currently 18 Dec 2018, 10:17

In Progress:

Admit Calls from Ross Join Chat Room | McCombs Join Chat Room for Latest Updates


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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

If n is an integer, then n is divisible by how many positive

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 24 Dec 2013, 02:48
6
16
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (01:10) correct 24% (01:20) wrong based on 843 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.

Data Sufficiency
Question: 3
Category: Arithmetic Properties of numbers
Page: 153
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 24 Dec 2013, 02:49
3
5
SOLUTION

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
For more on number properties check: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of two different prime numbers --> n=ab, where a and b are primes, so # of factors is (1+1)(1+1)=4. Sufficient.

(2) n and 2^3 are each divisible by the same number of positive integers --> 2^3 has 4 different positive factors (1, 2, 4, and 8) so n has also 4. Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Manager
Manager
avatar
Joined: 09 Apr 2013
Posts: 107
Location: India
WE: Supply Chain Management (Consulting)
GMAT ToolKit User
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 25 Dec 2013, 11:06
3
Statement 1: If n is a product of two prime number, then it must be divisible by 4 positive integers. Sufficient.

Statement 2: 2^3 is divisible by 4 positive integers and since n and 2^3 are divisible by same number of positive integers, this statement is sufficient as well.

Hence the answer is D.
_________________

+1 KUDOS is the best way to say thanks :-)

"Pay attention to every detail"

Intern
Intern
avatar
Joined: 22 Apr 2013
Posts: 5
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 26 Dec 2013, 21:52
IMO - A
To find the # of positive integers that divide n, we need to know the primes in n
(1) 2 primes For e.g. 3 and 5 so the n is 15 and divisible by 4 positive int (1,3,5 & 15) so suff.
(2) Not sure about statement 2
For e.g. 2^3 is 8.Now, if n is also 8 then sufficient.
But if n is 16 then even though both 2^3 and 16 are divisible by 4 positive numbers.n has one more positive int 16.so insuff.

Pls correct my understanding of stmt 2.Thanks
Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 146
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 27 Dec 2013, 18:36
1
himapm1l wrote:
IMO - A
To find the # of positive integers that divide n, we need to know the primes in n
(1) 2 primes For e.g. 3 and 5 so the n is 15 and divisible by 4 positive int (1,3,5 & 15) so suff.
(2) Not sure about statement 2
For e.g. 2^3 is 8.Now, if n is also 8 then sufficient.
But if n is 16 then even though both 2^3 and 16 are divisible by 4 positive numbers.n has one more positive int 16.so insuff.

Pls correct my understanding of stmt 2.Thanks

It should be D mate.... Statement 2 is also sufficient. More information can be found here: math-number-theory-88376.html
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 30 Dec 2013, 02:11
If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.

Sol:
Given n is an integer and so n is divisible by how many positive integers or how many factors does n have.

Using st 1, we have n is the product of 2 different prime numbers a and b
so n =ab....let a =2 b =3 then n =6 = 2^1 *3^1 and no. of factors of n are 4 ( 1,2,3 and 6)

Consider n is of the form n = a^2*b then n= 12 and no. of factors are 6 (1,2,3,4,6 and 12 )
St 1 is not sufficient as n is a multiple of 2 prime nos. but to what powers are the prime nos. raised, we don't know. Hence A and D are ruled out

In general, when a no. p can be represented by the form p= q^a*r^b*z^c where q,r and z are prime factors raised to the powers a, b and c respectively then the number of factors will be (a+1)*(b+1)*(c+1)


St 2 says n and 2^3 ie 8 have same factors which is 4. Hence no. of factors of n are 4

Ans B.
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 260
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 02 Jun 2014, 13:56
Hi Bunuel, In statement-1, how do we know that the powers of two prime numbers is 1? I interpreted st-1 as n is a product of two different primes but their powers could be anything. So n could be ab, a^1*b, or a*b^1. Not Sufficient.
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 03 Jun 2014, 07:43
2
MensaNumber wrote:
Hi Bunuel, In statement-1, how do we know that the powers of two prime numbers is 1? I interpreted st-1 as n is a product of two different primes but their powers could be anything. So n could be ab, a^1*b, or a*b^1. Not Sufficient.


Well, first of all \(a^1*b=a*b^1=ab\).

As for the powers: ask yourself can we says that 12=2^2*3 is the product of two different prime numbers? No.

n is the product of two different prime numbers means n = (prime 1)*(prime 2).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 260
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 03 Jun 2014, 07:50
Bunuel wrote:
Well, first of all \(a^1*b=a*b^1=ab\).


Haha! Off course. Thats why silly errors are killing me. :)

Bunuel wrote:
As for the powers: ask yourself can we says that 12=2^2*3 is the product of two different prime numbers? No.

n is the product of two different prime numbers means n = (prime 1)*(prime 2).

Hope it's clear.


Yes makes sense. thanks!
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Intern
Intern
avatar
B
Joined: 15 Sep 2014
Posts: 10
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 28 Nov 2016, 03:39
D:

1. n = 1. p1 Xp2 so 3 . Sufficient
2. n and 2^3 implies, 2X2X2 so 3. sufficient
hence D

Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers.

Data Sufficiency
Question: 3
Category: Arithmetic Properties of numbers
Page: 153
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
Senior Manager
Senior Manager
avatar
P
Joined: 17 Mar 2014
Posts: 375
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 09 Jun 2017, 10:26
Bunuel wrote:
SOLUTION

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.


Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
For more on number properties check: http://gmatclub.com/forum/math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

If n is an integer, then n is divisible by how many positive integers?

(1) n is the product of two different prime numbers --> n=ab, where a and b are primes, so # of factors is (1+1)(1+1)=4. Sufficient.

(2) n and 2^3 are each divisible by the same number of positive integers --> 2^3 has 4 different positive factors (1, 2, 4, and 8) so n has also 4. Sufficient.

Answer: D.


Hi Bunuel

Here, are not we only considering positive factors. What about negative factors ?

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9207
Premium Member
Re: If n is an integer, then n is divisible by how many positive  [#permalink]

Show Tags

New post 10 Aug 2018, 15:33
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If n is an integer, then n is divisible by how many positive &nbs [#permalink] 10 Aug 2018, 15:33
Display posts from previous: Sort by

If n is an integer, then n is divisible by how many positive

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.