January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday. January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 23 Jun 2008
Posts: 138

If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
05 Feb 2010, 11:51
Question Stats:
69% (00:54) correct 31% (01:00) wrong based on 1953 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52345

Re: GMAT Prep  Prime Number
[#permalink]
Show Tags
05 Feb 2010, 12:11




Manager
Joined: 26 May 2005
Posts: 188

Re: GMATPrep
[#permalink]
Show Tags
06 Apr 2010, 21:55
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




Manager
Joined: 13 Dec 2009
Posts: 224

Re: GMAT Prep  Prime Number
[#permalink]
Show Tags
12 Mar 2010, 05:35
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: doneanddusted730q49v40



Manager
Joined: 24 Jul 2009
Posts: 242

Re: multiples and prime: help please
[#permalink]
Show Tags
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...!!



Magoosh GMAT Instructor
Affiliations: Magoosh
Joined: 28 Nov 2011
Posts: 31
Location: United States (CA)

Re: no.prop
[#permalink]
Show Tags
19 Dec 2011, 14:43
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



Manager
Joined: 27 Feb 2012
Posts: 119

Re: If n is a multiple of 5 and n=(p^2)q, where p and q are prim
[#permalink]
Show Tags
19 Jan 2013, 02:17
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.



Senior Manager
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: if n is a multiple of 5 ...
[#permalink]
Show Tags
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 25b. q^2   P can be a multiple of 25c. pq  PQ is definitely a multiple of 5 but it not necessarily a multiple of 25d. (P^2)(q^2)  Correcte. (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
Joined: 17 Jul 2013
Posts: 47
GPA: 3.74

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
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?



Math Expert
Joined: 02 Sep 2009
Posts: 52345

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
27 Aug 2014, 04:12
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 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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 03 Feb 2013
Posts: 848
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

If is n is multiple of 5, and n=p^2*q where p and q are prime, w
[#permalink]
Show Tags
20 Dec 2014, 09:49
Lets say p^2 * q = 5 Then only q^2 and p^2 *q^2 can be 25 > All other options are eliminated. Lets say p^2 * q = 25 then q^2 is eliminated. Hence D)
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



Current Student
Joined: 20 Jan 2017
Posts: 58
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
26 Jan 2017, 15:47
1) Since n consists of two prime numbers p and q and it divisible by 5, either p or q have to be 5. 2) If we square both p and q, and one of them is 5, the product will have to be divisible by 5^2=25.
The correct answer is D.



Director
Joined: 02 Sep 2016
Posts: 678

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
03 Apr 2017, 09:21
n is of the form 5a where a is any positive integer. p or q is 5, otherwise n cannot be a multiple of 5. So to be sure that the answer is a multiple of 25, p^2q^2 is the right answer. For example, if p=5 then p^2 will be a multiple of 25 and same for q.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



Manager
Joined: 02 Jan 2017
Posts: 73
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
11 Dec 2017, 03:26
Bunuel 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. \(p^3q\)
\(n=5k\) 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. Can this be done with this approach, that prime factors of a perfect square will have even powers? By this theory, only D option meets the criteria. Correct me if I am wrong.



Math Expert
Joined: 02 Sep 2009
Posts: 52345

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
11 Dec 2017, 03:53
mtk10 wrote: Bunuel 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. \(p^3q\)
\(n=5k\) 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. Can this be done with this approach, that prime factors of a perfect square will have even powers? By this theory, only D option meets the criteria. Correct me if I am wrong. A multiple of 25 is not necessarily a perfect square. For example, 75 is a multiple of 25 but is not a perfect square.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4596
Location: United States (CA)

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
12 Dec 2017, 07:06
balboa wrote: 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 A common phrase that is used on the GMAT is the word must. In this question, we are asked which of the following must be a multiple of 25. This means that one of our answer choices will always be a multiple of 25, no matter what. It is our job to determine which one, based on the given information. We are given that n is a multiple of 5, n = (p^2)q, and that p and q are prime numbers. Because n is a multiple of 5, a prime number, we know that either p or q is 5. Let’s now analyze each answer choice to determine which one MUST (in all cases) be a multiple of 25. A) p^2 If p = 3, then p^2 = 9 is not a multiple of 25. Answer choice A is not correct. B) q^2 If q = 3, then q^2 = 9 is not a multiple of 25. Answer choice B is not correct. C) pq If p = 5 and q = 3 (or vice versa), pq = 15 is not a multiple of 25. Answer choice C is not correct. D) (p^2)(q^2) Regardless of which values we select for p and q, since we know that either p or q is 5, (p^2)(q^2) will always be a multiple of 25. If this is too difficult to see, let’s use numbers. If p = 5 and q = 3, (p^2)(q^2) = (25)(9) is a multiple of 25. If p = 3 and q = 5, (p^2)(q^2) = (9)(25) is also a multiple of 25. Answer choice D is correct. For practice, let’s analyze answer choice E. E) (p^3)q If p = 3 and q = 5, then (p^3)q = 135 is not a multiple of 25. Answer choice E is not correct. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13368
Location: United States (CA)

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
16 Jan 2018, 12:36
Hi All, This question is built around a couple of Number Properties and can be solved by TESTing VALUES. To start, we're told two things about N... 1) N is a multiple of 5 2) N = (P)(P)(Q) Since N is a multiple of 5, at least one of it's prime factors MUST be a 5. We're told that P and Q are both PRIME, which means that P or Q or both will be a multiple of 5. This is an interesting point, since the question asks which of the following MUST be a multiple of 25 (meaning  which of these answers will ALWAYS be a multiple of 25 no matter how many different examples you can come up with?). As such, we will have to consider a couple of different possibilities... IF... P = 5 Q = 2 N = 50 We can eliminate answers B and C. IF.... P = 2 Q = 5 N = 20 We can eliminate answers A and E. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



NonHuman User
Joined: 09 Sep 2013
Posts: 9459

Re: If is n is multiple of 5, and n=p^2*q where p and q are prim
[#permalink]
Show Tags
20 Jan 2019, 10:47
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




Re: If is n is multiple of 5, and n=p^2*q where p and q are prim &nbs
[#permalink]
20 Jan 2019, 10:47






