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

It is currently 25 Sep 2018, 22:16

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

M30-14

  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: 49493
M30-14  [#permalink]

Show Tags

New post 16 Sep 2014, 01:45
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (00:55) correct 45% (01:41) wrong based on 69 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49493
Re M30-14  [#permalink]

Show Tags

New post 16 Sep 2014, 01:45
1
1
Official Solution:


If \(p\) is a positive integer, is \(p\) a prime number?

(1) \(p\) and \(p+1\) have the same number of factors.

Primes have 2 factors, 1 and itself, (the reverse is also true: if a positive integer has 2 factors, then it must be a prime). So, for the answer to the question to be YES, both \(p\) and \(p+1\) must be primes. Are there consecutive primes? Yes, 2 and 3.

Could we have a case when \(p\) and \(p+1\) have the same number of factors, and \(p\) is NOT a prime? Yes. For example, both 14 (not a prime) and 15 have four factors. Also, both 21 (not a prime) and 22 have four factors.

Not sufficient.

(2) \(p-1\) is a factor of \(p\).

\(p-1\) and \(p\) are consecutive integers. Consecutive integers do not share any common factor but 1. Therefore, for \(p-1\) to be a factor of \(p\), \(p-1\) must be 1, which makes \(p\) equal to prime number 2. Sufficient.


Answer: B
_________________

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

Manager
Manager
avatar
Joined: 23 Jan 2012
Posts: 67
Re: M30-14  [#permalink]

Show Tags

New post 30 Sep 2014, 16:26
1
Bunuel, can you please advise with 2 mins/question how do we quickly determine that 14 and 15 or 21 and 22 could satisfy condition A? Although I did it correctly, I took more than 4 mins to solve this question.
Intern
Intern
avatar
Joined: 09 Feb 2015
Posts: 7
Re: M30-14  [#permalink]

Show Tags

New post 05 Jun 2015, 00:06
p2bhokie wrote:
Bunuel, can you please advise with 2 mins/question how do we quickly determine that 14 and 15 or 21 and 22 could satisfy condition A? Although I did it correctly, I took more than 4 mins to solve this question.

yes this is a valid question..please explain sir.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49493
Re: M30-14  [#permalink]

Show Tags

New post 05 Jun 2015, 04:54
harshalnamdeo88 wrote:
p2bhokie wrote:
Bunuel, can you please advise with 2 mins/question how do we quickly determine that 14 and 15 or 21 and 22 could satisfy condition A? Although I did it correctly, I took more than 4 mins to solve this question.

yes this is a valid question..please explain sir.


You should spend some time and TEST values.
_________________

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

Intern
Intern
avatar
Joined: 25 Apr 2015
Posts: 10
Re: M30-14  [#permalink]

Show Tags

New post 10 Jan 2016, 13:12
Bunuel wrote:
Official Solution:


If \(p\) is a positive integer, is \(p\) a prime number?

(1) \(p\) and \(p+1\) have the same number of factors.

Primes have 2 factors, 1 and itself, (the reverse is also true: if a positive integer has 2 factors, then it must be a prime). So, for the answer to the question to be YES, both \(p\) and \(p+1\) must be primes. Are there consecutive primes? Yes, 2 and 3.

Could we have a case when \(p\) and \(p+1\) have the same number of factors, and \(p\) is NOT a prime? Yes. For example, both 14 (not a prime) and 15 have four factors. Also, both 21 (not a prime) and 22 have four factors.

Not sufficient.

(2) \(p-1\) is a factor of \(p\).

\(p-1\) and \(p\) are consecutive integers. Consecutive integers do not share any common factor but 1. Therefore, for \(p-1\) to be a factor of \(p\), \(p-1\) must be 1, which makes \(p\) equal to prime number 2. Sufficient.


Answer: B


What if P=1 than P-1=0 won't this make statement 2 insufficient?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49493
Re: M30-14  [#permalink]

Show Tags

New post 10 Jan 2016, 13:14
rhio wrote:
Bunuel wrote:
Official Solution:


If \(p\) is a positive integer, is \(p\) a prime number?

(1) \(p\) and \(p+1\) have the same number of factors.

Primes have 2 factors, 1 and itself, (the reverse is also true: if a positive integer has 2 factors, then it must be a prime). So, for the answer to the question to be YES, both \(p\) and \(p+1\) must be primes. Are there consecutive primes? Yes, 2 and 3.

Could we have a case when \(p\) and \(p+1\) have the same number of factors, and \(p\) is NOT a prime? Yes. For example, both 14 (not a prime) and 15 have four factors. Also, both 21 (not a prime) and 22 have four factors.

Not sufficient.

(2) \(p-1\) is a factor of \(p\).

\(p-1\) and \(p\) are consecutive integers. Consecutive integers do not share any common factor but 1. Therefore, for \(p-1\) to be a factor of \(p\), \(p-1\) must be 1, which makes \(p\) equal to prime number 2. Sufficient.


Answer: B


What if P=1 than P-1=0 won't this make statement 2 insufficient?


0 is not a factor of any integer.
_________________

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

Intern
Intern
avatar
B
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
M30-14  [#permalink]

Show Tags

New post 17 Apr 2017, 06:34
Bunuel wrote:
harshalnamdeo88 wrote:
p2bhokie wrote:
Bunuel, can you please advise with 2 mins/question how do we quickly determine that 14 and 15 or 21 and 22 could satisfy condition A? Although I did it correctly, I took more than 4 mins to solve this question.

yes this is a valid question..please explain sir.


You should spend some time and TEST values.


You can at least think about the rule that the number of factors is the multiplication of the possibilities of the powers of its prime factors.

e.g. \(14=2^1*7^1\), power possibilities are \(2^0, 2^1\) and \(7^0, 7^1\), which multiplicates in \(2*2=4 factors\)

e.g. \(15=3^1*5^1\), power possibilities are \(3^0, 3^1\) and \(5^0, 5^1\), which multiplicates in \(2*2=4 factors\)
Intern
Intern
avatar
B
Joined: 13 Oct 2017
Posts: 39
Re: M30-14  [#permalink]

Show Tags

New post 05 Mar 2018, 03:42
Hi Bunuel,

Can you recap the rules for 0 again please?

I also got this question wrong because I thought of p=1 and p-1 = 0 for statement 2.

So in effect 0 is a multiple of all numbers but not a factor of any number?

Best wishes,

Tosin
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49493
Re: M30-14  [#permalink]

Show Tags

New post 05 Mar 2018, 04:28
ttaiwo wrote:
Hi Bunuel,

Can you recap the rules for 0 again please?

I also got this question wrong because I thought of p=1 and p-1 = 0 for statement 2.

So in effect 0 is a multiple of all numbers but not a factor of any number?

Best wishes,

Tosin


0 is not a factor of any integer: division by 0 is not allowed.

0 is a multiple of every integer: 0/integer = 0.
_________________

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

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1813
Reviews Badge CAT Tests
Re: M30-14  [#permalink]

Show Tags

New post 06 Mar 2018, 05:20
If \(p\) is a positive integer, is \(p\) a prime number?


(1) \(p\) and \(p+1\) have the same number of factors.

Let p =2 & p+1 =3.............P is prime..............Answer is Yes

Let P = 21 & p+1=22..........P is Not Prime........Answer is NO

( For clarification: factors of 21: 1,3,7,21 & factors of 22: 1,2,11,22)..the each have 4 factors)

Insufficient

(2) \(p-1\) is a factor of \(p\).

This means that the number before p is a factor of P. This happens only in one case when P = 2.

Then P is prime = 2

Sufficient

Answer: B

Note: Two consecutive numbers have no common factor except 1.
GMAT Club Bot
Re: M30-14 &nbs [#permalink] 06 Mar 2018, 05:20
Display posts from previous: Sort by

M30-14

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


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®.