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

 It is currently 17 Nov 2019, 23:15

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

If n = 4p, where p is a prime number greater than 2, how many differen

Author Message
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173
If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

27 Dec 2012, 05:55
10
1
79
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:22) correct 43% (01:25) wrong based on 1916 sessions

HideShow timer Statistics

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: 59095
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

27 Dec 2012, 05:59
12
24
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.

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.
_________________
Retired Moderator
Joined: 29 Oct 2013
Posts: 248
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

Updated on: 02 Jun 2014, 01:59
6
7
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?
_________________

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

Originally posted by NoHalfMeasures on 01 Jun 2014, 22:06.
Last edited by NoHalfMeasures on 02 Jun 2014, 01:59, edited 1 time in total.
General Discussion
Manager
Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

21 Apr 2013, 00:04
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! - Rumi

http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprep-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 - http://gmatclub.com/forum/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542
Math Expert
Joined: 02 Sep 2009
Posts: 59095
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

21 Apr 2013, 04:06
Transcendentalist wrote:
Is one not a divisor?

It is but its' not even (how many different positive even divisors does n have, including n).
_________________
Intern
Joined: 30 Jan 2014
Posts: 12
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

04 Mar 2014, 03:45
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: 59095
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

04 Mar 2014, 03:53
1
2
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?
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

04 Mar 2014, 21:19
1
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 "+1 Kudos" to appreciate
Director
Joined: 03 Aug 2012
Posts: 656
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

19 Apr 2014, 23:35
1
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.
Math Expert
Joined: 02 Sep 2009
Posts: 59095
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

02 Jun 2014, 00:04
MensaNumber wrote:
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?

_________________
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 416
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

17 Apr 2015, 02:36
if we apply theory of finding number of divisor
Let,s plug in p= 3
then n= 12
Factor of 12 are 3, 2, 2
p>2, so 2s are out
Now the formula (p+1)+(q+1)+(r+1) = 3+1 = 4
Ans C
_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

27 Jul 2015, 01:10
ITMRAHUL 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) 2
b) 3
c) 4
d) 6
e) 8

can some 1 throw light on it?

@p=3, n = 4*3 = 12, Positive Even divisor of n = {2, 4, 6, 12} i.e. 4 Divisors
@p=5, n = 4*5 = 20, Positive Even divisor of n = {2, 4, 10, 20} i.e. 4 Divisors
@p=7, n = 4*7 = 28, Positive Even divisor of n = {2, 4, 14, 28} i.e. 4 Divisors
@p=11, n = 4*11 = 44, Positive Even divisor of n = {2, 4, 22, 44} i.e. 4 Divisors
@p=13, n = 4*13 = 52, Positive Even divisor of n = {2, 4, 26, 52} i.e. 4 Divisors
and so on...

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15468
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

21 Aug 2015, 11:16
2
1
Hi All,

This question can be solved rather easily by TESTing VALUES:

We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12

The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?

12:
1,12
2,6
3,4

How many of these divisors are EVEN? 2, 4, 6, 12 …..4 even divisors.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15468
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

03 Sep 2015, 22:47
Hi All,

This question can be solved rather easily by TESTing VALUES:

We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12

The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?

12:
1,12
2,6
3,4

How many of these divisors are EVEN? 2, 4, 6, and 12 …..that's a total of 4 even divisors.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 07 Mar 2014
Posts: 16
Location: India
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

26 Oct 2015, 03:07
3
n = 4p
p prime no. $$> 2$$

We have to find the no. of even divisors which means even factors of n

P must be a odd no. because 2 is the only even prime no.

Let p be $$3$$

$$n= 4 * 3$$

= $$2^{2} * 3$$

Now , No of factors of P = $$2^{2+1} * 3^{1+1}$$ = $$2^{3} * 3^{2}$$

= $$3 * 2 = 6$$

Even factors = Total factors - odd factors

To find Odd factors we take all the prime apart from 2. so here we are left with only 3

Odd factors = $$3^{1+1} = 3^{2}= 2$$

Total factors - Odd factors = Even factors
$$6-2 = 4$$

Math Expert
Joined: 02 Sep 2009
Posts: 59095
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

22 Jan 2016, 10:03
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 REVOLUTION VIDEO SOLUTION:

_________________
Current Student
Joined: 02 Sep 2015
Posts: 51
Location: United States
GMAT 1: 760 Q49 V44
GPA: 3.97
WE: Project Management (Energy and Utilities)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

01 Jun 2016, 08:47
Since p is primes and is > 2, then p must be an odd number since 2 is the only even prime number.

I solved by simply plugging in:
p = 5 (a prime) ---> n = 20
Factors of 20 include:
20 1
10 2
5 4

In this factor tree there is a total of 4 even factors means C is the correct answer.

If you aren't convinced after this you should have time to plug in another prime number for p. I finished within 50 seconds using just p =5.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8394
Location: United States (CA)
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

13 Jul 2016, 07:39
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

This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:

n = 4 x 3

n = 12

Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.

1, 12, 6, 2, 4, 3

From this we see that we have 4 even divisors: 12, 6, 2, and 4.

If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so

n = 4 x 5

n = 20

The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.

No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Current Student
Joined: 12 Aug 2015
Posts: 2549
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

28 Dec 2016, 08:16
One of those Quality Questions from the Official Guide.
here is my solution =>
Method 1->
n=2^2*p
as p is a odd prime (all primes >2 are odd)
number of even factors => 2*2-> four
Four factors are -> 2,4,2p,4p
Alternatively let p=3
so n=12
factors => 1,2,3,4,6,12
even factors => 2,4,6,12
hence four

Hence C

_________________
Director
Joined: 02 Sep 2016
Posts: 643
Re: If n = 4p, where p is a prime number greater than 2, how many differen  [#permalink]

Show Tags

01 Apr 2017, 07:09
n=4p
Let;s factorize n
n= 2^2 * p^a (a is some positive power of p and we know that p is a prime number greater than 2 i.e. it is odd as the only even prime number is 2. So we don't have to worry about the power of p as it would yield odd integer and we have to just find even factors.)

Thus the answer is 2, 4(2^2), 2p (even), and 4p (even).
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Re: If n = 4p, where p is a prime number greater than 2, how many differen   [#permalink] 01 Apr 2017, 07:09

Go to page    1   2    Next  [ 23 posts ]

Display posts from previous: Sort by