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

It is currently 04 May 2016, 08:37
GMAT Club Tests

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

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1459
Followers: 6

Kudos [?]: 193 [1] , given: 0

p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 18 Aug 2007, 09:00
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

20% (03:28) correct 80% (02:13) wrong based on 58 sessions

HideShow timer Statictics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: p-a-q-b-r-c-s-d-x-where-x-is-a-perfect-square-if-p-q-r-126645.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Dec 2014, 10:26, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1264
Location: Madrid
Followers: 27

Kudos [?]: 225 [0], given: 0

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 18 Aug 2007, 09:20
bkk145 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


If they are distinct, a b c and d must be positive even integers.
(1) Not sufficient
x could be (pqrs)^18 and p,q r s may or may not be distinct

(2) As ab is not divisible by 4, a and b are not both even. Thus p,q,r,s are not distinct SUFF
Manager
Manager
avatar
Joined: 08 Jan 2007
Posts: 67
Location: D.C.
Followers: 1

Kudos [?]: 1 [0], given: 0

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 18 Aug 2007, 10:18
This is a tough one for me, can someone explain futher please
Manager
Manager
User avatar
Joined: 15 Aug 2007
Posts: 70
Followers: 2

Kudos [?]: 5 [0], given: 0

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 18 Aug 2007, 10:20
kevincan wrote:
bkk145 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


If they are distinct, a b c and d must be positive even integers.
(1) Not sufficient
x could be (pqrs)^18 and p,q r s may or may not be distinct

(2) As ab is not divisible by 4, a and b are not both even. Thus p,q,r,s are not distinct SUFF


Further Explanation...

Will go for B...
In 2nd
As ab and cd is not divisible by 4, a and b both are not even no.Similarly c and d both are not even no. But in a and b, one would be even number.Also in c and d, one would be even number.So 2 variables (In p,q,r,s)can be different,whose squares are even but 2 should be same to make it a perfect square..

Need more explanation ????
2 KUDOS received
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3385
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 14

Kudos [?]: 223 [2] , given: 2

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 19 Aug 2007, 12:09
2
This post received
KUDOS
bkk145 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


OK let me begin with statement 2..its the easiest to work out

if X is a perfect square then P^a...s^d all have to be raised to an even power..

4 is not a factor of ab clearly tells me that one of these powers either a or b or c or d is not even..if thats the case then one of the primes is repeated..


therefore 2 is sufficient

I have trouble with 1...

so again same approach

18 is a factor..well which means that if 18*2 is 36...which is an even power then we can have possible repeat of prime factors...and possibly not..say p^6 Q^6 r^6s^6 is a perfect square...now p and q =2 or could be 3 or 2...we dont know..INSUFF...

B it is..
1 KUDOS received
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1459
Followers: 6

Kudos [?]: 193 [1] , given: 0

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 20 Aug 2007, 18:13
1
This post received
KUDOS
1
This post was
BOOKMARKED
OA=B

Answer
When a perfect square is broken down into its prime factors, those prime factors always come in "pairs." For example, the perfect square 225 (which is 15 squared) can be broken down into the prime factors 5 × 5 × 3 × 3. Notice that 225 is composed of a pair of 5's and a pair of 3's.

The problem states that x is a perfect square. The prime factors that build x are p, q, r, and s. In order for x to be a perfect square, these prime factors must come in pairs. This is possible if either of the following two cases hold:

Case One: The exponents a, b, c, and d are even. In the example 3^2 5^4 7^2 11^6, all the exponents are even so all the prime factors come in pairs.

Case Two: Any odd exponents are complemented by other odd exponents of the same prime. In the example 3^1 5^4 3^3 11^6, notice that 3^1 and 3^3 have odd exponents but they complement each other to create an even exponent (3^4), or "pairs" of 3's. Notice that this second case can only occur when p, q, r, and s are NOT distinct. (In this example, both p and r equal 3.)

Statement (1) tells us that 18 is a factor of both ab and cd. This does not give us any information about whether the exponents a, b, c, and d are even or not.

Statement (2) tells us that 4 is not a factor of ab and cd. This means that neither ab nor cd has two 2's as prime factors. From this, we can conclude that at least two of the exponents (a, b, c, and d) must be odd. As we know from Case 2 above, if paqbrcsd is a perfect square but the exponents are not all even, then the primes p, q, r and s must NOT be distinct.

The correct answer is B: Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 03 Jun 2007
Posts: 384
Followers: 2

Kudos [?]: 11 [1] , given: 0

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 21 Aug 2007, 08:50
1
This post received
KUDOS
Amazing problem bkk. I totally missed the "odd" part of the explanation. Awesome.
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2756
Location: New York City
Followers: 9

Kudos [?]: 594 [0], given: 4

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 24 Jan 2008, 10:47
fresinha12 wrote:
bkk145 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


OK let me begin with statement 2..its the easiest to work out

if X is a perfect square then P^a...s^d all have to be raised to an even power..

4 is not a factor of ab clearly tells me that one of these powers either a or b or c or d is not even..if thats the case then one of the primes is repeated..

therefore 2 is sufficient

I have trouble with 1...

so again same approach

18 is a factor..well which means that if 18*2 is 36...which is an even power then we can have possible repeat of prime factors...and possibly not..say p^6 Q^6 r^6s^6 is a perfect square...now p and q =2 or could be 3 or 2...we dont know..INSUFF...

B it is..

thanks. very helpful
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3580
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 474

Kudos [?]: 2711 [0], given: 359

GMAT ToolKit User Premium Member
Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 24 Jan 2008, 11:54
Expert's post
good question and answers
\(+1^2\)
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9280
Followers: 455

Kudos [?]: 115 [0], given: 0

Premium Member
Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 11 Dec 2014, 08:16
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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32616
Followers: 5651

Kudos [?]: 68611 [0], given: 9816

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are [#permalink]

Show Tags

New post 11 Dec 2014, 10:27
Expert's post
1
This post was
BOOKMARKED
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.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: p-a-q-b-r-c-s-d-x-where-x-is-a-perfect-square-if-p-q-r-126645.html
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Re: p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r, and s are   [#permalink] 11 Dec 2014, 10:27
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Is the positive integer x a perfect square? Bunuel 3 21 Apr 2016, 00:42
1 Experts publish their posts in the topic If x is a perfect square, is x also a perfect cube? Bunuel 2 15 Apr 2016, 01:22
2 Experts publish their posts in the topic Is x/p(p 2 + q 2 + r 2 ) = x carcass 5 03 Feb 2013, 18:45
21 Experts publish their posts in the topic p^a*q^b*r^c*s^d=x, where x is a perfect square. If p, q, r enigma123 19 28 Jan 2012, 00:00
7 Experts publish their posts in the topic Is P + Q > R + S ? paam0101 7 09 Jul 2010, 13:13
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.