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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

6

This post received KUDOS

Expert's post

6

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.

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

3

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 _________________

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

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

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! _________________

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

Re: If n is a multiple of 5 and n=(p^2)q, where p and q are prim [#permalink]
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

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

Re: if n is a multiple of 5 ... [#permalink]
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

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

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

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). _________________

If is n is multiple of 5, and n=p^2*q where p and q are prime, w [#permalink]
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) _________________

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...