Author
Message
TAGS:
Manager

Joined: 02 Dec 2012

Posts: 178

Followers: 2

Kudos [? ]:
175
[1 ] , given: 0

If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
27 Dec 2012, 04:55
1

This post received KUDOS

2

This post was BOOKMARKED

Question Stats:

50% (02:01) correct

50% (00:56) wrong

based on 303 sessions
If n = 4p, where p is a prime number greater than 2, how many different positive

even divisors does n have, including n ?

(A) Two

(B) Three

(C) Four

(D) Six

(E) Eight

Math Expert

Joined: 02 Sep 2009

Posts: 18737

Followers: 3243

Kudos [? ]:
22383
[3 ] , given: 2616

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
27 Dec 2012, 04:59
3

This post received KUDOS

Walkabout wrote:

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight

Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positive

even divisors will 4p have.

p = 3 --> 4p = 12--> 12 has 4 even divisors: 2, 4, 6, and 12.

Answer: C.

Or this way: since p is prime greater than 2, then p=odd, thus 4p=even, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

Similar question to practice:

if-n-is-a-prime-number-greater-than-3-what-is-the-remainder-137869.html Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 11 Rules for Posting!!! RESOURCES: [GMAT MATH BOOK ]; 1. Triangles ; 2. Polygons ; 3. Coordinate Geometry ; 4. Factorials ; 5. Circles ; 6. Number Theory ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager

Joined: 27 Jan 2013

Posts: 58

Location: India

Concentration: Social Entrepreneurship, Operations

GMAT 1 : 740 Q50 V40

GPA: 3.51

WE: Other (Transportation)

Followers: 2

Kudos [? ]:
18
[1 ] , given: 33

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
12 Apr 2013, 23:08
1

This post received KUDOS

Bunuel wrote:

Walkabout wrote:

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight

Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positive

even divisors will 4p have.

p = 3 --> 4p = 12--> 12 has 4 even divisors: 2, 4, 6, and 12.

Answer: C.

Or this way: since p is prime greater than 2, then p=odd, thus 4p=odd, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

Similar question to practice:

if-n-is-a-prime-number-greater-than-3-what-is-the-remainder-137869.html Hope it helps.

Hi Bunnel

Just a small typo in the explanation

Or this way: since p is prime greater than 2, then p=odd,

thus 4p=odd, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

It should be 4p = Even

Cheers

Math Expert

Joined: 02 Sep 2009

Posts: 18737

Followers: 3243

Kudos [? ]:
22383
[1 ] , given: 2616

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
13 Apr 2013, 02:49
1

This post received KUDOS

Dipankar6435 wrote:

Bunuel wrote:

Walkabout wrote:

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight

Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positive

even divisors will 4p have.

p = 3 --> 4p = 12--> 12 has 4 even divisors: 2, 4, 6, and 12.

Answer: C.

Or this way: since p is prime greater than 2, then p=odd, thus 4p=odd, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

Similar question to practice:

if-n-is-a-prime-number-greater-than-3-what-is-the-remainder-137869.html Hope it helps.

Hi Bunnel

Just a small typo in the explanation

Or this way: since p is prime greater than 2, then p=odd,

thus 4p=odd, which means that it has 4 even divisors: 2, 4, 2p, and 4p.

It should be 4p = Even

Cheers

Typo edited. Thank you. +1.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 11 Rules for Posting!!! RESOURCES: [GMAT MATH BOOK ]; 1. Triangles ; 2. Polygons ; 3. Coordinate Geometry ; 4. Factorials ; 5. Circles ; 6. Number Theory ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager

Joined: 24 Nov 2012

Posts: 161

Concentration: Sustainability, Entrepreneurship

GMAT 1 : 770 Q50 V44

WE: Business Development (Internet and New Media)

Followers: 12

Kudos [? ]:
65
[0 ] , given: 73

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
20 Apr 2013, 23:04

Is one not a divisor?

_________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumihttp://www.manhattangmat.com/blog/index ... nprep-com/ - This is worth its weight in gold Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013 GMAT - 770, Q50, V44, Oct 7th, 2013 My Debrief - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

Math Expert

Joined: 02 Sep 2009

Posts: 18737

Followers: 3243

Kudos [? ]:
22383
[0 ] , given: 2616

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
21 Apr 2013, 03:06

Intern

Joined: 30 Jan 2014

Posts: 17

Followers: 0

Kudos [? ]:
0
[0 ] , given: 15

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
04 Mar 2014, 02:45

p can get any prime number greater than 2 so there should be unlimited different divisor for the n because p can be 11,13,17,19.... What is wrong with this ?

Math Expert

Joined: 02 Sep 2009

Posts: 18737

Followers: 3243

Kudos [? ]:
22383
[0 ] , given: 2616

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
04 Mar 2014, 02:53
lool wrote:

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? (A) Two (B) Three (C) Four (D) Six (E) Eight p can get any prime number greater than 2 so there should be unlimited different divisor for the n because p can be 11,13,17,19.... What is wrong with this ?

No matter which prime p is, 4p will have only four EVEN divisors: 2, 4, 2p, and 4p. Try to check it with any prime greater than 2.

Does this make sense?

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 11 Rules for Posting!!! RESOURCES: [GMAT MATH BOOK ]; 1. Triangles ; 2. Polygons ; 3. Coordinate Geometry ; 4. Factorials ; 5. Circles ; 6. Number Theory ; 7. Remainders ; 8. Overlapping Sets ; 9. PDF of Math Book ; 10. Remainders ; 11. GMAT Prep Software Analysis NEW!!! ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!! ; 12. Tricky questions from previous years. NEW!!! ;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 ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director

Status: The Best Or Nothing

Joined: 27 Dec 2012

Posts: 655

Location: India

Concentration: General Management, Technology

WE: Information Technology (Computer Software)

Followers: 3

Kudos [? ]:
147
[0 ] , given: 162

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
04 Mar 2014, 20:19

lool wrote:

p can get any prime number greater than 2 so there should be unlimited different divisor for the n because p can be 11,13,17,19.... What is wrong with this ?

4 has two even divisors >> 2 & 4

Any prime no p divisors will have 2p & 4p (from above)

So total = 4

_________________

Kindly press "Kudos" to appreciate

Director

Joined: 03 Aug 2012

Posts: 883

Concentration: General Management, General Management

GMAT 1 : 630 Q47 V29GMAT 2 : 680 Q50 V32

GPA: 3.7

Followers: 11

Kudos [? ]:
161
[0 ] , given: 299

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
19 Apr 2014, 22:35

n=4*p

And p(prime) > 2

n= 2*2*p

Positive even divisors 'n' can have including 'n':

2

2p

4

4p which is also equal to 'n'

Hence 4 positive even divisors.

_________________

Rgds, TGC! _____________________________________________________________________I Assisted You => KUDOS Please _____________________________________________________________________________

Manager

Joined: 29 Oct 2013

Posts: 158

Concentration: Finance

GMAT 1 : 750 Q48 V46GMAT 2 : Q V0

GRE 1 : 327 Q161 V166

GPA: 3.7

WE: Corporate Finance (Retail Banking)

Followers: 3

Kudos [? ]:
86
[0 ] , given: 102

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
01 Jun 2014, 21:06

n= 4p = 2^2*p^1

so total no. of factors: (2+1)*(1+1)= 6

total no. of odd factors, since p is odd as it is a prime>2: p^1 and p^0 = 2

Total no. of even factors: 6 - 2 = 4

Now if n was n=4pq where p and q are both prime no.s greater than 2 then:

total no. of factors: (2+1)*(1+1)*(1+1)= 12

total no. of odd factors, since p is odd as it is a prime>2: (1+1)*(1+1)= 4

Total no. of even factors: 12 - 4 = 8

Hi Bunuel, could you validate my logic pls?

_________________

Please consider giving 'kudos' if you like my post and want to thank Read about my journey to 750 here - a-non-native-speakers-journey-to-99-le-on-verbal-750overall-171722.html#p1367876

Last edited by

MensaNumber on 02 Jun 2014, 00:59, edited 1 time in total.

Math Expert

Joined: 02 Sep 2009

Posts: 18737

Followers: 3243

Kudos [? ]:
22383
[0 ] , given: 2616

Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink ]
01 Jun 2014, 23:04

Re: If n = 4p, where p is a prime number greater than 2, how man
[#permalink ]
01 Jun 2014, 23:04

Similar topics
Author
Replies
Last post
Similar Topics:

12
If n = 4p, where p is a prime number greater than 2, how man
tinman1412
9
24 Aug 2007, 08:41

If n=4p, where p is a prime number greater than2, how many
iamba
3
24 Jun 2007, 20:21

If n=4p, where p is a prime number greater than 2, how many
cucrose
8
16 Jan 2007, 10:31

If n = 4p, where p is a prime number greater than 2, how
desiguy
7
10 Dec 2005, 19:30

If n = 4p, where p is a prime number greater than 2 how many
Priti
8
14 Aug 2005, 12:43