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

It is currently 16 Apr 2014, 23:14

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

If x, y, and z are integers greater than 1, and (3^27)(35^10

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
Joined: 19 Aug 2007
Posts: 169
Followers: 1

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

If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] New post 14 Dec 2007, 12:31
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

40% (02:39) correct 59% (01:15) wrong based on 42 sessions
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

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

Last edited by Bunuel on 31 Mar 2014, 00:23, edited 2 times in total.
Added the OA.
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3599
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 324

Kudos [?]: 1573 [0], given: 354

GMAT ToolKit User GMAT Tests User Premium Member
 [#permalink] New post 14 Dec 2007, 13:58
Expert's post
jimjohn wrote:
oh sorry guys i didnt notice that the exponents didnt appear. plz note the edited question


In this case: D

5^2*z=3*x^y

1. z is prime and is 3. So, x=5 SUFF.

2. x is prime and is 5. So, x=5 SUFF.



but (327)*(3510)*(z) = (58)*(710)*(914)*(xy) is a top-level problem :-D
Manager
Manager
Joined: 01 Nov 2007
Posts: 83
Followers: 0

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

Re: DS - primes [#permalink] New post 14 Dec 2007, 18:20
jimjohn wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime



(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y)
re-written as
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y)
simplified to
25z=3(x^y) x^y is an integer, multiple of 25 so z is a multiple of 3

I z prime, so 3; x=5
II x is prime, x^y multiple of 25 so x can only be 5

D
Manager
Manager
Joined: 19 Aug 2007
Posts: 169
Followers: 1

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

 [#permalink] New post 14 Dec 2007, 19:29
ok so i understand up until 25 * z = 3 * (x^y)

now how do we know that z has to be a multiple of 3. is it because we know that 3 is a factor of 25 * z, and since 3 is not a factor of 25 then it has to be a factor of z.

is there such a rule like that, that if x is a factor of a*b, then x has to be a factor of one of a or b.

thx
Manager
Manager
User avatar
Joined: 21 Oct 2013
Posts: 243
Followers: 2

Kudos [?]: 48 [0], given: 120

If x, y, and z are integers greater than 1 and (3^27)(35^10) [#permalink] New post 20 Mar 2014, 13:44
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime
(2) x is prime


OE:
[Reveal] Spoiler:
(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y) Break up the 35^10 and simplify the 9^14
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y) Divide both sides by common terms 5^8, 7^10, 3^27
(5^2)(z) = (3)(x^y)

(1) SUFFICIENT: z must have a factor of 3 to balance the 3 on the right side of the equation.
(1) says that z is prime, so z cannot have another factor besides the 3. Therefore z = 3.
Since z = 3, the left side of the equation is 75, so x^y = 25.
The only integers greater than 1 that satisfy this equation are x = 5 and y = 2, so (1) is sufficient.
Put differently, the expression x^y must provide the two fives that we have on the left side of the equation.
The only way to get two fives if x and y are integers greater than 1 is if x = 5 and y = 2.

(2) SUFFICIENT: x must have a factor of 5 to balance out the 5^2 on the left side.
Since (2) says that x is prime, x cannot have any other factors, so x = 5.


Hi, can anyone explain how this works, please.
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4170
Location: Pune, India
Followers: 894

Kudos [?]: 3785 [0], given: 148

Re: If x, y, and z are integers greater than 1 and (3^27)(35^10) [#permalink] New post 20 Mar 2014, 21:09
Expert's post
goodyear2013 wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime
(2) x is prime


OE:
[Reveal] Spoiler:
(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y) Break up the 35^10 and simplify the 9^14
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y) Divide both sides by common terms 5^8, 7^10, 3^27
(5^2)(z) = (3)(x^y)

(1) SUFFICIENT: z must have a factor of 3 to balance the 3 on the right side of the equation.
(1) says that z is prime, so z cannot have another factor besides the 3. Therefore z = 3.
Since z = 3, the left side of the equation is 75, so x^y = 25.
The only integers greater than 1 that satisfy this equation are x = 5 and y = 2, so (1) is sufficient.
Put differently, the expression x^y must provide the two fives that we have on the left side of the equation.
The only way to get two fives if x and y are integers greater than 1 is if x = 5 and y = 2.

(2) SUFFICIENT: x must have a factor of 5 to balance out the 5^2 on the left side.
Since (2) says that x is prime, x cannot have any other factors, so x = 5.


Hi, can anyone explain how this works, please.


Split everything into prime factors:

(3^{27})(35^{10})(z) = (5^8)(7^{10})(9^{14})(x^y)

(3^{27})(5^{10})(7^{10})*(z) = (3^{28})(5^8)(7^{10})(x^y)

Now powers of prime factors on both sides of the equation should match since all variables are integers. If you have only 3^{27} on left hand side, it cannot be equal to the right hand side which has 3^{28}. Prime factors cannot be created by multiplying other numbers together and hence you must have the same prime factors with the same powers on both sides of the equation.

Stmnt 1: z is prime
Note that you have 3^{28} on Right hand side but only 3^{27} on left hand side. This means z must have at least one 3. Since z is prime, z MUST be 3 only. You get

(3^{28})(5^{10})(7^{10}) = (3^{28})(5^8)(7^{10})(x^y)

Now 5^2 is missing on the right hand side since we have 5^{10} on left hand side but only 5^8 on right hand side. So x^y must be 5^2. x MUST be 5.
Sufficient.

Stmnt2: x is prime
If x is prime, it must be 5 since 5^2 is missing on the right hand side. This would give us x^y = 5^2. Sufficient.

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2869

Kudos [?]: 18344 [0], given: 2345

GMAT Tests User CAT Tests
Re: If x, y, and z are integers greater than 1 and (3^27)(35^10) [#permalink] New post 21 Mar 2014, 00:44
Expert's post
goodyear2013 wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime
(2) x is prime


OE:
[Reveal] Spoiler:
(3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y) Break up the 35^10 and simplify the 9^14
(3^27)(5^10)(7^10)(z) = (5^8)(7^10)(3^28)(x^y) Divide both sides by common terms 5^8, 7^10, 3^27
(5^2)(z) = (3)(x^y)

(1) SUFFICIENT: z must have a factor of 3 to balance the 3 on the right side of the equation.
(1) says that z is prime, so z cannot have another factor besides the 3. Therefore z = 3.
Since z = 3, the left side of the equation is 75, so x^y = 25.
The only integers greater than 1 that satisfy this equation are x = 5 and y = 2, so (1) is sufficient.
Put differently, the expression x^y must provide the two fives that we have on the left side of the equation.
The only way to get two fives if x and y are integers greater than 1 is if x = 5 and y = 2.

(2) SUFFICIENT: x must have a factor of 5 to balance out the 5^2 on the left side.
Since (2) says that x is prime, x cannot have any other factors, so x = 5.


Hi, can anyone explain how this works, please.


Similar question to practice: if-x-y-and-z-are-integers-greater-than-1-and-90644.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Intern
Intern
Joined: 14 Mar 2014
Posts: 2
Followers: 0

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

Re: [#permalink] New post 30 Mar 2014, 11:23
walker wrote:
jimjohn wrote:
1. z is prime and is 3. So, x=5 SUFF.


Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1

Thanks!
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2869

Kudos [?]: 18344 [0], given: 2345

GMAT Tests User CAT Tests
Re: Re: [#permalink] New post 31 Mar 2014, 00:26
Expert's post
karimtajdin wrote:
walker wrote:
jimjohn wrote:
1. z is prime and is 3. So, x=5 SUFF.


Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1

Thanks!


Notice that we are told that x, y, and z are integers greater than 1, hence x=25 and y=1 is not possible.

Check here for a complete solution: if-x-y-and-z-are-integers-greater-than-1-and-57122.html#p1346892

Similar question to practice: if-x-y-and-z-are-integers-greater-than-1-and-90644.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Intern
Intern
Joined: 14 Mar 2014
Posts: 2
Followers: 0

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

Re: Re: [#permalink] New post 31 Mar 2014, 05:02
Bunuel wrote:
we are told that x, y, and z are integers greater than 1


Oh! Can't believe I missed that! It makes sense now :). Thanks!
Re: Re:   [#permalink] 31 Mar 2014, 05:02
    Similar topics Author Replies Last post
Similar
Topics:
New posts If x, y, and z are integers greater than 1, and chineseburned 2 18 May 2008, 14:41
New posts If x, y, and z are integers greater than 1, and arjtryarjtry 2 30 Jul 2008, 06:07
New posts If x, y, and z are integers greater than 1, and dancinggeometry 3 22 Sep 2008, 01:03
New posts If x, y, and z are integers greater than 1, and kairoshan 3 18 Nov 2009, 20:46
This topic is locked, you cannot edit posts or make further replies. New If x, y, and z are integers greater than 1 and (3^27)(35^10) goodyear2013 0 21 Mar 2014, 00:44
Display posts from previous: Sort by

If x, y, and z are integers greater than 1, and (3^27)(35^10

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.