Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Oct 2014, 15:56

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If is n is multiple of 5, and n=p^2*q where p and q are prim

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 23 Jun 2008
Posts: 140
Followers: 3

Kudos [?]: 25 [0], given: 0

If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink] New post 05 Feb 2010, 11:51
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (01:55) correct 33% (01:00) wrong based on 348 sessions
If is n is multiple of 5, and n=p^2*q where p and q are prime, which of the following must be a multiple of 25?

A. p^2
B. q^2
C. pq
D. p^2*q^2
E. p^3*q
[Reveal] Spoiler: OA
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28794 [5] , given: 2849

Re: GMAT Prep - Prime Number [#permalink] New post 05 Feb 2010, 12:11
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
If n is multiple of 5, and n = p^2q where p and q are prime, which of the following must be a multiple of 25?

A p^2
B. q^2
C. pq
D. p^2q^2
E. p^3q

n=5k and n=p^2p, (p and q are primes).
Q: 25m=?

Well obviously either p or q is 5. As we are asked to determine which choice MUST be multiple of 25, right answer choice must have BOTH, p and q in power of 2 or higher to guarantee the divisibility by 25. Only D offers this.

Answer: D.
_________________

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

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Dec 2009
Posts: 264
Followers: 10

Kudos [?]: 111 [1] , given: 13

Reviews Badge
Re: GMAT Prep - Prime Number [#permalink] New post 12 Mar 2010, 05:35
1
This post received
KUDOS
If n is a multiple of 5 and n = p^2*q, where p and q are prime numbers which of the following must be a multiple of 25

n is a multiple of 5 and p and q are prime numbers.
the only prime number which multiple of 5 i s5 itself
so either p or q is 5
This is why we can surely say that p^2*q^2 is the multiple of 25 since one of thme is 5 and 5^2 = 25
so d is the answer
_________________

My debrief: done-and-dusted-730-q49-v40

2 KUDOS received
Manager
Manager
avatar
Joined: 26 May 2005
Posts: 210
Followers: 2

Kudos [?]: 71 [2] , given: 1

Re: GMATPrep [#permalink] New post 06 Apr 2010, 21:55
2
This post received
KUDOS
n is a multiple of 5
n = pq^2 and p and q are primes numbers... so either p or q is 5 or both are 5

A. p^2 -- q could be 5, so this might not be a multiple of 25
B. q^2 -- p could be 5, so this might not be a multiple of 25
C. pq -- p could be 5 and q some other prime number,so this might not be a multiple of 25
D. p^2q^2 -- bingo, either p or q has to be 5, and this one sure will be a multiple of 25
E.p^3q - q could be 5, so this might not be a multiple of 25

D
Senior Manager
Senior Manager
avatar
Joined: 24 Jul 2009
Posts: 298
Followers: 2

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

Re: multiples and prime: help please [#permalink] New post 18 Apr 2010, 12:43
MMMs wrote:
Sorry (in advance) if I'm not posting this in the right place. Not sure I quite figured what to post where...
Could someone help me with this question? TIA!

If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2
b) q^2
c) pq
d) p^2q^2
e) p^3q


IMHO D

if n is a multiple of 5, it means [/m]p^2q[/m]is multiple of 5. Now both p and q are prime, so atleast one of them should be 5.

let say if p=5, then and q=3, (n=75) ,then option b is out. >>> [/m]3^2[/m] is not a multiple of 25.
let say if p=3, then and q=5, (n=45) ,then option a is out. >>> [/m]3^2[/m] is not a multiple of 25.
let say if p=3, then and q=5, (n=45) ,then option c is out. >>> 3 * 5 is not a multiple of 25.
let say if p=3, then and q=5, (n=135) ,then option e is out. >>>[/m]3^3 * 5[/m] is not a multiple of 25.

Let see option D.

Both p or q can be 5, and if any one of them is squared, the result will be divisible by 5...!!
Expert Post
3 KUDOS received
Magoosh GMAT Instructor
User avatar
Affiliations: Magoosh
Joined: 28 Nov 2011
Posts: 31
Location: United States (CA)
Followers: 211

Kudos [?]: 210 [3] , given: 5

Re: no.prop [#permalink] New post 19 Dec 2011, 14:43
3
This post received
KUDOS
Expert's post
For this question, it's best to look at the equation and the conditions together. Here's what we know:
1. n must be a multiple of 5
2. n=p^2*q
3. p and q are prime numbers.

For n to be a multiple of 5, either p or q has to be 5. They can't be 10, 15, 25, etc. since they have to be prime numbers. As long as one of the two is 5, the other can be any prime number. Knowing this, take a look at the answer choices:

A. p^2
B. q^2
C. pq
D.p^2*q^2
E.p^3*q

A and B should be eliminated, because the question asks "which of the following MUST be a multiple of 25", which means for whatever values we put in that fulfill the conditions in the stem, the correct answer choice should be 25. A and B are both at risk of either p or q being the "other" prime number (p=5 and q=3, p=3 and q=5) in which case 9 won't be divisible by 25.

C is also out-- we can finagle p and q into both being 5 to make this true, but it will not be true for every case, since p or q can just as easily be 3, and 15 won't be divisible by 25.

D is the correct answer because regardless of what p or q may be individually, the fact is that one of them will always have to be 5 and thus the result of p^2*q^2 will always be divisible by 25, which is what we're looking for in the correct answer.

E is incorrect because it's actually very similar to C, where we can potentially make it divisible by 25, but it won't be true for every case.

I hope that helps, feel free to let me know if you have any other questions!
_________________

Margarette
Magoosh Test Prep

Image

Image

Senior Manager
Senior Manager
avatar
Joined: 13 May 2011
Posts: 324
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 19

Kudos [?]: 136 [0], given: 11

Re: no.prop [#permalink] New post 19 Dec 2011, 21:54
with the given conditions: either p or q has be 5. now picking number for each answer: only D satisfies.
Manager
Manager
avatar
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 32 [0], given: 12

GMAT ToolKit User
Re: no.prop [#permalink] New post 20 Dec 2011, 03:16
fro me its D P^2*q^2
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2011
Posts: 276
Followers: 0

Kudos [?]: 24 [0], given: 110

Re: no.prop [#permalink] New post 05 Jan 2012, 03:40
Clear D. As already discussed above, others may not always be divisible by 25.
_________________

Consider KUDOS if you feel the effort's worth it

Intern
Intern
avatar
Joined: 04 Aug 2011
Posts: 45
Location: United States
Concentration: Technology, Leadership
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 14 [0], given: 20

Re: If is n is multiple of 5, and n=p^2*q where p and q are [#permalink] New post 15 Jan 2012, 15:45
D is the correct answer.
Tip - whenever given like n = 5k, and n = pq, always check the possibility of both p and Q as 5. I did only for 1 variable and got the answer wrong then later Bunnel post helped.
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 191
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 2

Kudos [?]: 45 [0], given: 4

Re: If is n is multiple of 5, and n=p^2*q where p and q are [#permalink] New post 18 Apr 2012, 18:56
either p or q can be the prime 5 so squaring both numbers shows the term must be divisible by 25
_________________

DETERMINED TO BREAK 700!!!

1 KUDOS received
Manager
Manager
avatar
Joined: 27 Feb 2012
Posts: 138
Followers: 1

Kudos [?]: 20 [1] , given: 22

Re: If n is a multiple of 5 and n=(p^2)q, where p and q are prim [#permalink] New post 19 Jan 2013, 02:17
1
This post received
KUDOS
kiyo0610 wrote:
If n is a multiple of 5 and n=(p^2)q, where p and q are prime numbers, which of the following must be a multiple of 25 ?

(a)p^2
(b)q^2
(c)pq
(d)(p^2)(q^2)
(e)(p^3)q


either p = 5 or q = 5
Simply go to options
a) p = 2 say and q = 5
b) q =2 and p = 5
c) p =2 and q =5
d) either of p or q is 5 so this will be multiple of 25
e) p = 2 and q =5


So only D stands
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink] New post 21 Jan 2013, 06:51
In order to be a multiple of 25 we must have 5*5 derived somewhere from the equation. Also for n to be a factor of 5 the number 5 must be either p or q.

The only answer that MUST have 25 as an outcome of either p or q is D.
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 508
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 395 [0], given: 241

Re: if n is a multiple of 5 ... [#permalink] New post 24 Jul 2013, 17:26
if n is a multiple of 5 and n=P^2q,where p and g are prime numbers, which of the following must be a multiple of 25?
a. p^2 - q can be a multiple of 25

b. q^2 - - P can be a multiple of 25

c. pq - PQ is definitely a multiple of 5 but it not necessarily a multiple of 25

d. (P^2)(q^2) - Correct

e. (P^3)(q) - Assuming the worst case scenario (P is some other prime number except 5), Q is definitely a multiple of 5 but it not necessarily a multiple of 25
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Intern
Intern
avatar
Joined: 17 Jul 2013
Posts: 17
GRE 1: 326 Q166 V160
Followers: 0

Kudos [?]: 2 [0], given: 13

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink] New post 27 Aug 2014, 03:39
My question is that what if n in the following question stem is equal to p^(2q), instead of (p^2)(q). how would the answer change.... My reasoning goes like this:

Since p raised to some integer power means p.p.p.p..... up to 2q. (1) and since (1) is divisible by 5, p must be divisible by 5. Hence, p^2 must be divisible by 25. Is this reasoning correct?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28794 [0], given: 2849

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim [#permalink] New post 27 Aug 2014, 04:12
Expert's post
megatron13 wrote:
If n is multiple of 5, and n = p^2q where p and q are prime, which of the following must be a multiple of 25?

A p^2
B. q^2
C. pq
D. p^2q^2
E. p^3q

My question is that what if n in the following question stem is equal to p^(2q), instead of (p^2)(q). how would the answer change.... My reasoning goes like this:

Since p raised to some integer power means p.p.p.p..... up to 2q. (1) and since (1) is divisible by 5, p must be divisible by 5. Hence, p^2 must be divisible by 25. Is this reasoning correct?


Yes, if we were told that p^(2q) is a multiple of 5 where p and q are primes, then p must be 5, which will guarantee divisibility by 25 of each option but B (q^2) and C (pq).
_________________

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

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim   [#permalink] 27 Aug 2014, 04:12
    Similar topics Author Replies Last post
Similar
Topics:
If n is a multiple of 5 and n=p^2 *q, where p and q are tarek99 2 07 Dec 2007, 05:15
If n is a multiple of 5 and n=p^2 . q where p and q are Finding Perdition 1 13 Aug 2007, 01:44
1 IF N IS A MULTIPLE OF 5 AND N=(P^2) *Q , WHERE P AND Q ARE buffett76 1 28 May 2007, 04:14
If n is a multiple of 5 and n=p^2*q , where p adn q are dinesh8 3 29 Apr 2006, 01:08
If n is a multiple of 5 and n=p^2q, where p and q are prime jodeci 2 07 Apr 2006, 19:20
Display posts from previous: Sort by

If is n is multiple of 5, and n=p^2*q where p and q are prim

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.