It is currently 17 Nov 2017, 18:17

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x, y, and z are integers greater than 1, and

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

Hide Tags

6 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 356

Kudos [?]: 418 [6], given: 47

GMAT ToolKit User
If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 21 Feb 2010, 14:20
6
This post received
KUDOS
32
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:23) correct 61% (01:34) wrong based on 1344 sessions

HideShow timer Statistics

If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?

(1) y is prime.
(2) x is prime.
[Reveal] Spoiler: OA

_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~


Last edited by Bunuel on 08 Oct 2012, 04:18, edited 2 times in total.
Edited the question.

Kudos [?]: 418 [6], given: 47

Manager
Manager
avatar
Joined: 26 May 2005
Posts: 203

Kudos [?]: 133 [0], given: 1

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 22 Feb 2010, 11:19
(327)(510)(z) = (58)(914)(xy)

3 * 109 * 3 * 17 * 2 * 5 * z = 2 * 29 * 2 * 457 * x * y (all the numbers are prime)

x = (3^2 * 5 * 17 * 109 * z) / (29 * 2 * 457 * y) (cancelling 2 on numerator and denominator)

1) y is prime
Not sufficient
y = 3, z = 29*2*457 * n (where n is an intereger ) and values of x could vary depending on n or depending on y(3,5,109, 457 etc)
(2) x is prime
Not sufficient
y = 9 * 5 * 17,z = 29*2*457 , x = 109
y = 9 * 5 * 109,z = 29*2*457 , x = 17

combining .. there is no value of x that will satify the equation as if y is prime, then y could be any of the values of 3,5, 17, 109 or a different number that is a factor of z. and if z is an interger, x cannot be prime.

E ( not sure if E is the correct answer as there is no valid value of x that satisfies the conditions)

Kudos [?]: 133 [0], given: 1

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2757

Kudos [?]: 1908 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: If x, y, and z are integers [#permalink]

Show Tags

New post 24 Feb 2010, 16:29
IMO C

Reduced equation becomes

\(\frac{25*z}{3^{15}*x}\) = y

now if y is prime

z can be 3^15 and x = 5 or z = 2* 3^15 and x = 10 thus not sufficient

now if x is prime same explanation above.

now take both x and y prime, in this case x can be only 5 and z = 3^15

thus it should be C
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1908 [0], given: 235

Manager
Manager
avatar
Joined: 26 May 2005
Posts: 203

Kudos [?]: 133 [0], given: 1

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 24 Feb 2010, 16:36
Here's the solution for the re-posted problem :lol:
If x, y, and z are integers greater than 1, and 3^27 * 5^10 * z =5^8 * 9^14 * x * y , then what is the value of x?
3^27 * 5^10 * z =5^8 * 9^14 * x * y
3^27 * 5^ 10 * z = 5^ 8 * 3^28 * x * y
5^2 * z = 3 * x * y
x = (5^2 * z) / 3y

(1) y is prime
y can be a factor of z, and z can be a factor of y and there could be a lot of possibilities of x
y = 3, z = 27, x = 75
y = 5, z = 3, x = 5
Not sufficient
(2) x is prime
z has to be a multiple of 3 and y has to be a multiple of 5
z= 3*a (where a is prime not equal to 5), y = 25, then x=a(many values for a)
z=3, y = 5, x=5
Not sufficient

combining .. x and y both are prime .. and as 5^2 is in the numerator, y has to be 5 and z has be to 3 or else x cannot be prime.
y=5, z=3, x=5

C

Kudos [?]: 133 [0], given: 1

Senior Manager
Senior Manager
User avatar
Joined: 21 Jul 2009
Posts: 364

Kudos [?]: 199 [0], given: 22

Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Re: If x, y, and z are integers [#permalink]

Show Tags

New post 24 Feb 2010, 16:45
After simplifying the given question, we end up with 5*5*z/(3*y) = x.

Stmt 1 - y can take a whole lot of prime numbers from 2 to infinity (not the car!!!) and until we know z, we can't comment on value of x.

Stmt 2 - x itself can take a whole lot of prime numbers from 2 to infinity (again, not the car!!!) and we would have to struggle to get appropriate values for z and y, and there can very many that match the criteria.

Combining both stmts - as long as z is some composite, that can be expressed as a multiple of 3, x (any prime number choice) and y (prime number choice), it is good, and there are whole lot of possibilities for x as well.

I am not very sure, how do we get to B as the OA. In my opinion, it must be E. Math experts and Math God Bunuel might wish to throw some light!!!!
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

Kudos [?]: 199 [0], given: 22

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [4], given: 12324

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 24 Feb 2010, 17:19
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
jeeteshsingh wrote:
If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x*y\), then what is the value of x?

(1) y is prime

(2) x is prime

SOURCE: Manhattan tests

[Reveal] Spoiler: OA
B


Please explain in detail



If the answer is really B, then I think question should be: \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\). If I'm right, then it's B indeed.

In it's current form the answer is C as explained.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132517 [4], given: 12324

2 KUDOS received
Manager
Manager
avatar
Joined: 14 Jul 2010
Posts: 71

Kudos [?]: 34 [2], given: 2

GMAT ToolKit User
Re: If x, y, and z are integers [#permalink]

Show Tags

New post 01 Aug 2010, 16:31
2
This post received
KUDOS
I had this question in the test today too. I went with E but QA is B. I didnt understand the explanation. I think QA is wrong here, 2 is a prime too.


---

The best way to answer this question is to use the rules of exponents to simplify the question stem, then analyze each statement based on the simplified equation.

(327)(510)(z) = (58)(914)(xy) Simplify the 914
(327)(510)(z) = (58)(328)(xy) Divide both sides by common terms 58, 327
(52)(z) = 3xy

(1) INSUFFICIENT: Analyzing the simplified equation above, we can conclude that z must have a factor of 3 to balance the 3 on the right side of the equation. Similarly, x must have at least one factor of 5. Statement (1) says that y is prime, which does no tell us how many fives are contained in x and z.

For example, it is possible that x = 5, y = 2, and z = 3:
52 · 3 = 3 · 52

It is also possible that x = 25, y = 2, and z = 75:
52 · 75 = 3 · 252
52 · 52 · 3 = 3 · 252

(2) SUFFICIENT: Analyzing the simplified equation above, we can conclude that x must have a factor of 5 to balance out the 52 on the left side. Since statement (2) says that x is prime, x cannot have any other factors, so x = 5. Therefore statement (2) is sufficient.

The correct answer is B.

Kudos [?]: 34 [2], given: 2

1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2757

Kudos [?]: 1908 [1], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: If x, y, and z are integers [#permalink]

Show Tags

New post 02 Aug 2010, 04:31
1
This post received
KUDOS
what if y=25 , z=6 and x=2 ?
if y =5, x=5 and z=3 ?

for statement 2 both holds true..so B alone is not sufficient.
either OA is wrong or Question is wrong.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1908 [1], given: 235

Intern
Intern
avatar
Joined: 21 Jul 2010
Posts: 31

Kudos [?]: 9 [0], given: 3

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 02 Aug 2010, 04:50
The answer has to be C..

3^27 * 5^10 * z =5^8 * 9^14 * x * y
3^27 * 5^ 10 * z = 5^ 8 * 3^28 * x * y
5^2 * z = 3 * x * y
x = (5^2 * z) / 3y

after this..either of the statements ie..

1) X is prime

y and z can take a whole lot of values..

2) y is prime.

x and z can again take many values..prime or not prime..

hence only when we know that both x and y are prime
can we reach the answer that z=3, x=5,y=5

Kudos [?]: 9 [0], given: 3

Intern
Intern
avatar
Joined: 11 Jun 2011
Posts: 13

Kudos [?]: 2 [0], given: 6

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 27 Jun 2012, 09:36
Bunuel wrote:
jeeteshsingh wrote:
If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x*y\), then what is the value of x?

(1) y is prime

(2) x is prime

SOURCE: Manhattan tests

[Reveal] Spoiler: OA
B


Please explain in detail



If the answer is really B, then I think question should be: \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\). If I'm right, then it's B indeed.

In it's current form the answer is C as explained.


Bunuel, can you please explain the answer for choice B
_________________

_______________________________________________________________________________________________________________________________
If you like my solution kindly reward me with Kudos.

Kudos [?]: 2 [0], given: 6

Expert Post
10 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [10], given: 12324

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 28 Jun 2012, 02:53
10
This post received
KUDOS
Expert's post
10
This post was
BOOKMARKED
riteshgupta wrote:
Bunuel wrote:
jeeteshsingh wrote:
If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x*y\), then what is the value of x?

(1) y is prime

(2) x is prime

SOURCE: Manhattan tests

[Reveal] Spoiler: OA
B


Please explain in detail



If the answer is really B, then I think question should be: \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\). If I'm right, then it's B indeed.

In it's current form the answer is C as explained.


Bunuel, can you please explain the answer for choice B


You mean what would be the solution if it were x^y instead of xy?

If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?

\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\) --> \(3^{27}*5^{2}*z =3^{28}*x^y\) --> \(5^{2}*z = 3*x^y\) --> \(\frac{x^y}{z}=\frac{5^2}{3}\), so \(x^y\) is a multiple of 25 and \(z\) is a multiple of 3.

(1) y is prime. We can have that \(x=5\), \(y=2=prime\) and \(z=3\) OR \(x=10\), \(y=2=prime\) and \(z=12\)... Not sufficient.

(2) x is prime. Since \(x^y\) is a multiple of \(5^2\) and \(x\) is a prime, then \(x=5\). Sufficient.

Answer: B.

Hope it's clear.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132517 [10], given: 12324

Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 17

Kudos [?]: 2 [0], given: 1

Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 17 Jul 2012, 08:20
think the answer is B even as written?

Formula simplifies to 25z/3y = x or 25z/3x=y

1: y is prime; since 25z/3y yields an integer, does it not hold that 25/y = integer since 3 is not a factor of 25. If y is prime, it has to be 5 since 5^2 are the prime factors of 25. However, in order to know X, we need to know what z might be, and Z could be any number with 3 as a prime factor. Not sufficient.

2: x is prime; since 25z/3x yields an integer, 25/x is also an integer since 3 is not a factor of 25. Holding the same logic as in 1; x must be 5. Sufficient.

Please let me know if I am thinking about this wrong

Kudos [?]: 2 [0], given: 1

Current Student
avatar
Joined: 02 Jul 2012
Posts: 21

Kudos [?]: 3 [0], given: 0

Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 17 Jul 2012, 16:41
JohnGalt44 wrote:
think the answer is B even as written?

Formula simplifies to 25z/3y = x or 25z/3x=y

1: y is prime; since 25z/3y yields an integer, does it not hold that 25/y = integer since 3 is not a factor of 25. If y is prime, it has to be 5 since 5^2 are the prime factors of 25. However, in order to know X, we need to know what z might be, and Z could be any number with 3 as a prime factor. Not sufficient.

2: x is prime; since 25z/3x yields an integer, 25/x is also an integer since 3 is not a factor of 25. Holding the same logic as in 1; x must be 5. Sufficient.

Please let me know if I am thinking about this wrong


Yes you are thinking about it wrongly.
Why does 25/x have to be an integer? 3 is not a factor of 25, but it can be a factor of z, the other term in the numerator.
Hence, if you let y=5^2, then z=3x, and x=any prime you want it to be. Not sufficient

However taking (1)+(2), both x and y have to be prime and since you need to make 25 using 3*x*y, only way to do it is using x=y=5 and z=3. C.

Please give kudos if you like.


Also, can OP please change answer in spoiler to the correct one?

Kudos [?]: 3 [0], given: 0

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 556 [1], given: 11

Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 22 Jan 2013, 01:21
1
This post received
KUDOS
jeeteshsingh wrote:
If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?

(1) y is prime.
(2) x is prime.


\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\)
\(3*9^{13}*5^{10}*z = 5^8*9^{14}*x^y\)
\(5^2*z = 3*x^y\)
\(x^y = \frac{5^2*z}{3}\)

It's obvious that z has a factor of 3 to cancel out the denominator and x has 5 as a factor...

1. y is prime

Let y = 3: \(5^3 = \frac{5^2*(5*3)}{3}\) Thus, x=5
Let y = 3 and x contain 3: \(5^{3}*3^3 = \frac{5^2*(5*3^4)}{3}\) Thus, x=15

INSUFFICIENT.

2. x is prime.. Well it's obvious that x has 5 as a factor.. If it's prime then x = 5*1 = 5
SUFFICIENT.

Answer: B
_________________

Impossible is nothing to God.

Kudos [?]: 556 [1], given: 11

Intern
Intern
avatar
Joined: 30 Oct 2011
Posts: 46

Kudos [?]: 21 [0], given: 13

GMAT ToolKit User
Re: If x, y, and z are integers [#permalink]

Show Tags

New post 18 Jul 2013, 15:05
Bunuel wrote:

You mean what would be the solution if it were x^y instead of xy?

If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?

\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\) --> \(3^{27}*5^{2}*z =3^{28}*x^y\) --> \(5^{2}*z = 3*x^y\) --> \(\frac{x^y}{z}=\frac{5^2}{3}\), so \(x^y\) is a multiple of 25 and \(z\) is a multiple of 3.

(1) y is prime. We can have that \(x=5\), \(y=2=prime\) and \(z=3\) OR \(x=10\), \(y=2=prime\) and \(z=12\)... Not sufficient.

(2) x is prime. Since \(x^y\) is a multiple of \(5^2\) and \(x\) is a prime, then \(x=5\). Sufficient.

Answer: B.

Hope it's clear.


Bunuel, if the statement (1) were- Z (instead of Y) is prime then the answer should be 'D'? Thanks!

Kudos [?]: 21 [0], given: 13

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [0], given: 12324

Re: If x, y, and z are integers [#permalink]

Show Tags

New post 18 Jul 2013, 15:17
mneeti wrote:
Bunuel wrote:

You mean what would be the solution if it were x^y instead of xy?

If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?

\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\) --> \(3^{27}*5^{2}*z =3^{28}*x^y\) --> \(5^{2}*z = 3*x^y\) --> \(\frac{x^y}{z}=\frac{5^2}{3}\), so \(x^y\) is a multiple of 25 and \(z\) is a multiple of 3.

(1) y is prime. We can have that \(x=5\), \(y=2=prime\) and \(z=3\) OR \(x=10\), \(y=2=prime\) and \(z=12\)... Not sufficient.

(2) x is prime. Since \(x^y\) is a multiple of \(5^2\) and \(x\) is a prime, then \(x=5\). Sufficient.

Answer: B.

Hope it's clear.


Bunuel, if the statement (1) were- Z (instead of Y) is prime then the answer should be 'D'? Thanks!


Yes, that's correct.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132517 [0], given: 12324

Intern
Intern
avatar
Joined: 30 Apr 2010
Posts: 21

Kudos [?]: 18 [0], given: 2

Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 27 Oct 2013, 16:34
Came across this question just now, it's a good one to study exponents:
if 3^27.5^10.z = 9^14.5^8.x^y what is the value of x?
the statement can be further expanded becoming: 3^27.5^10.z = 3^28.5^8.x^y

1) y is prime, we can be tempted to say y = 2, this is true in the case where z = 3 then x becomes 5 but what if z = 15 =(5)(3) then x^y = ((5)(3))^3 where x = (5)(3) and y = 3 where y is still prime. So insufficient.

2) x is prime, this leaves no doubt that x must equal 5.

Kudos [?]: 18 [0], given: 2

Intern
Intern
avatar
Joined: 25 Apr 2010
Posts: 4

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

GMAT ToolKit User
Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 16 Mar 2014, 04:35
But it says x,y,z are integers so they should be a single digit .. why are we taking them as double digits .. ?

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [0], given: 12324

Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 16 Mar 2014, 05:13

Kudos [?]: 132517 [0], given: 12324

Intern
Intern
avatar
Joined: 09 Mar 2014
Posts: 2

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

Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 30 Mar 2014, 12:46
I think it goes this way...

In order for the 2 parts to be equal we need to have the power of 3 in one side equal to the power of 3 in the other one.Same goes for 5.So in the left one the power of 3 is 27 and in the other one is 28.So we need a 3.In the left one the power of 5 is 10 and in the right is 8.

If we know for sure that x is a prime then it z must be 3(because it cannot be 5^-2) and x has to be the 5 missing..!!!!

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

Re: If x, y, and z are integers greater than 1, and   [#permalink] 30 Mar 2014, 12:46

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

If x, y, and z are integers greater than 1, and

  new topic 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 | Emoji artwork provided by EmojiOne

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®.