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: Distinct Prime Integers [#permalink]
28 Jan 2012, 01:31

5

This post received KUDOS

Expert's post

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we cannot get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*3^6*2^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r [#permalink]
29 Jan 2012, 10:26

A silly question! If you loose on such a question, what score one should expect for quant? (By the way I understood what you explained here, Bunuel, but you would be there on exam day, right!

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r [#permalink]
29 Jan 2012, 16:47

1

This post received KUDOS

Expert's post

docabuzar wrote:

A silly question! If you loose on such a question, what score one should expect for quant? (By the way I understood what you explained here, Bunuel, but you would be there on exam day, right!

Or this is a silly post that adds no value. On the GMAT, only the experimental ones are silly. This is a pretty tough question. If you think it is an easy one, you should consider providing your own explanation - you will learn quite a bit when you try to teach someone. _________________

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r [#permalink]
30 Jan 2012, 02:39

You mis understood my statement. Or may be I wrote it in a wrong way.

What I meant was that I want to ask a silly question, i.e., if someone looses on such a question in GMAT what score he/she should expect. (Acutally I do understand bunuel's explanation to this Q, but I donot think that I will be able to re-produce the concept if this Q appears with some varaition in GMAT)

As far as this question is concerned, for me, it was very tough. I have always appreciated the knowledge bunuel (& for that matter anyone) expresses here in these forum esp the ease with which bunuel explains so many twists in a single question. I m still learning. Cheers!

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r [#permalink]
30 Jan 2012, 12:31

1

This post received KUDOS

Expert's post

docabuzar wrote:

You mis understood my statement. Or may be I wrote it in a wrong way.

What I meant was that I want to ask a silly question, ...

Oh, don't worry, no hard feelings whatsoever.

docabuzar wrote:

If someone looses on such a question in GMAT what score he/she should expect. (Acutally I do understand bunuel's explanation to this Q, but I donot think that I will be able to re-produce the concept if this Q appears with some varaition in GMAT)

As far as this question is concerned, for me, it was very tough. I have always appreciated the knowledge bunuel (& for that matter anyone) expresses here in these forum esp the ease with which bunuel explains so many twists in a single question. I m still learning. Cheers!

You are right, it's a quite hard question, probably 700+. So if one answers incorrectly to 1 or 2 of such questions he/she can still expect a pretty decent score. _________________

Re: Distinct Prime Integers [#permalink]
12 Mar 2012, 10:31

Bunuel wrote:

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we can not get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Answer: B.

Hope it's clear.

Hi Bunnel

From statement 2 how did you say that P Q R S are distinct primes as we have information only on a,b,c,d???

Re: Distinct Prime Integers [#permalink]
12 Mar 2012, 10:49

2

This post received KUDOS

Expert's post

kotela wrote:

Bunuel wrote:

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we can not get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Answer: B.

Hope it's clear.

Hi Bunnel

From statement 2 how did you say that P Q R S are distinct primes as we have information only on a,b,c,d???

Thanks in advance

Well, I'm saying exactly the opposite for (2): \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes.

As for the connection between a, b, c, d and p, q, r, s: if \(p\), \(q\), \(r\), and \(s\) are distinct primes, then \(a\), \(b\), \(c\), and \(d\) MUST be even (all of them).

From (2) we get that NOT all from \(a\), \(b\), \(c\), and \(d\) are even, hence \(p\), \(q\), \(r\), and \(s\) are NOT distinct.

Re: Distinct Prime Integers [#permalink]
18 Jul 2013, 05:17

1

This post received KUDOS

Bunuel wrote:

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we can not get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Answer: B.

Hope it's clear.

I have a doubt regarding this, above we have taken statement 1 has 2 cases first case : \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes.

Now how can we take this case? because it says that x is a perfect square so ultimately total powers of x should be odd, but in this case total powers of x is even , hence x is not a perfect square which contradicts what is given, so shouldn't this case be invalid. second case for statement 1 of course looks fine.

shouldn't our objective be to find x such that x is a perfect square and p q r s are not distinct and 18 is a factor of ab and cd if we can find such a case then we will have two cases of perfect square: one with distinct p q r s and other with non distinct p q r s hence insufficient

but here the first case for statement 1 x is not a perfect square so how can we take this as a valid case ,or am I missing something, can anyone help?

Re: Distinct Prime Integers [#permalink]
18 Jul 2013, 06:30

1

This post received KUDOS

stne wrote:

Bunuel wrote:

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we can not get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Answer: B.

Hope it's clear.

I have a doubt regarding this, above we have taken statement 1 has 2 cases first case : \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes.

Now how can we take this case? because it says that x is a perfect square so ultimately total powers of x should be odd, but in this case total powers of x is even , hence x is not a perfect square which contradicts what is given, so shouldn't this case be invalid. second case for statement 1 of course looks fine.

shouldn't our objective be to find x such that x is a perfect square and p q r s are not distinct and 18 is a factor of ab and cd if we can find such a case then we will have two cases of perfect square: one with distinct p q r s and other with non distinct p q r s hence insufficient

but here the first case for statement 1 x is not a perfect square so how can we take this as a valid case ,or am I missing something, can anyone help?

Re: Distinct Prime Integers [#permalink]
18 Jul 2013, 06:57

1

This post received KUDOS

Expert's post

stne wrote:

Bunuel wrote:

enigma123 wrote:

\(p^a q^b r^c s^d=x\), where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cd

Any idea how to solve this question please? I don't have an OA unfortunately.

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

First of all: a perfect square always has even powers of its prime factors. So, if \(p\), \(q\), \(r\), and \(s\) ARE distinct primes, then in order \(x\) to be a perfect square \(a\), \(b\), \(c\), and \(d\) MUST be even.

(1) 18 is a factor of ab and cd --> we can not get whether \(a\), \(b\), \(c\), and \(d\) are even or odd. For example we can have following two cases: \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. \(p^a*q^b*r^c*s^d=2^2*3^{18}*5^2*7^{18}\): in this case \(p\), \(q\), \(r\), and \(s\) are distinct primes. Not sufficient.

(2) 4 is not a factor of ab and cd --> which means that at least one from \(a\) and \(b\), and at least one from \(c\) and \(d\) is NOT even (if for example \(a\) and \(b\) were BOTH even then \(ab\) would be a multiple of 4) --> \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes. Sufficient.

Answer: B.

Hope it's clear.

I have a doubt regarding this, above we have taken statement 1 has 2 cases first case : \(p^a*q^b*r^c*s^d=2^3*2^6*3^3*3^6\): in this case \(p\), \(q\), \(r\), and \(s\) are NOT distinct primes.

Now how can we take this case? because it says that x is a perfect square so ultimately total powers of x should be odd, but in this case total powers of x is even , hence x is not a perfect square which contradicts what is given, so shouldn't this case be invalid. second case for statement 1 of course looks fine.

shouldn't our objective be to find x such that x is a perfect square and p q r s are not distinct and 18 is a factor of ab and cd if we can find such a case then we will have two cases of perfect square: one with distinct p q r s and other with non distinct p q r s hence insufficient

but here the first case for statement 1 x is not a perfect square so how can we take this as a valid case ,or am I missing something, can anyone help?

Thanks

It was a typo. Edited. Should have been: \(p^a*q^b*r^c*s^d=2^3*3^6*2^3*3^6\). Thank you. +1. _________________

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r [#permalink]
09 Feb 2014, 05:17

Very good question. Thanks for posting. I chose the wrong answer. BUT If p,q,r & s are distinct primes then a,b,c,d each should be even. if one of them is odd (let's say a) then at least one more of them must also be odd and two of the primes must be equal otherwise the value x cannot be a perfect square. Knowing if one of a,b,c & d is odd answers the question. Hence B. I hope I made sense. _________________

Click on Kudos if you liked the post!

Practice makes Perfect.

gmatclubot

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r
[#permalink]
09 Feb 2014, 05:17

How the growth of emerging markets will strain global finance : Emerging economies need access to capital (i.e., finance) in order to fund the projects necessary for...

One question I get a lot from prospective students is what to do in the summer before the MBA program. Like a lot of folks from non traditional backgrounds...