If x, y, and z are integers greater than 1, and (3^27)(35^10 : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 12:51

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

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

Kudos [?]: 51 [1] , given: 0

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

### Show Tags

14 Dec 2007, 12:31
1
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:12) correct 57% (01:24) wrong based on 620 sessions

### HideShow timer Statistics

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.
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 547

Kudos [?]: 3558 [4] , given: 360

### Show Tags

14 Dec 2007, 13:58
4
KUDOS
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
Manager
Joined: 01 Nov 2007
Posts: 82
Followers: 0

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

### Show Tags

14 Dec 2007, 18:20
2
KUDOS
1
This post was
BOOKMARKED
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
Joined: 19 Aug 2007
Posts: 169
Followers: 1

Kudos [?]: 51 [0], given: 0

### Show Tags

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
Senior Manager
Joined: 21 Oct 2013
Posts: 419
Followers: 15

Kudos [?]: 1372 [0], given: 289

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

### Show Tags

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
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2134

Kudos [?]: 13653 [6] , given: 222

Re: If x, y, and z are integers greater than 1 and (3^27)(35^10) [#permalink]

### Show Tags

20 Mar 2014, 21:09
6
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 36567 Followers: 7081 Kudos [?]: 93196 [0], given: 10553 Re: If x, y, and z are integers greater than 1 and (3^27)(35^10) [#permalink] ### Show Tags 21 Mar 2014, 00:44 Expert's post 2 This post was BOOKMARKED 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. _________________ Intern Joined: 14 Mar 2014 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: [#permalink] ### Show Tags 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 Joined: 02 Sep 2009 Posts: 36567 Followers: 7081 Kudos [?]: 93196 [0], given: 10553 Re: Re: [#permalink] ### Show Tags 31 Mar 2014, 00:26 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. _________________ Intern Joined: 14 Mar 2014 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: Re: [#permalink] ### Show Tags 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! Senior Manager Joined: 10 Mar 2013 Posts: 290 GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39 Followers: 11 Kudos [?]: 98 [0], given: 2405 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 01 Sep 2014, 16:11 Can anyone explain whether my approach is valid? 5^2*z = 3*x^y (x^y)/z = (5^2)/3 = (5^2a)/(3a) x^y = 5^2a z = 3a (1) z is prime, so a = 1 and x^y = 25 => x = 5 S (2) x is prime, so a = 1 and z = 3 S D GMAT Club Legend Joined: 09 Sep 2013 Posts: 13456 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 09 Oct 2015, 07:37 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. _________________ Manager Joined: 01 Jan 2015 Posts: 63 Followers: 0 Kudos [?]: 60 [1] , given: 14 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 09 Oct 2015, 13:31 1 This post received KUDOS VeritasPrepKarishma wrote: 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) I just wanted to point out that $$x^y = 5^2$$ is not necessarily true. In fact, if the question asked for the value of y, then statement 2 would have been insufficient $$(3^{27})(35^{10})*(z) = (5^8)(7^{10})(9^{14})(x^y)$$ can be rewritten as $$\frac{(5^2 *z)}{3}=x^y$$ Written in this form, it is easy to notice that z must be a multiple of 3 since $$x^y$$ is an integer. Since it is given that x is prime, the prime factorization of $$x^y$$ will be x repeated y times, which means z should have at most one 3. Statement 2 doesn't require z to be prime, it could have a prime factorization of one 3 with any number of 5's and x must be 5, but y could take many integer values besides 2. For example: z=3*$$5^2$$, x=5, y=4 z=3*$$5^3$$, x=5, y=5 z=3*$$5^4$$, x=5, y=6 x must be 5, so statement 2 is sufficient. Manager Joined: 01 Jan 2015 Posts: 63 Followers: 0 Kudos [?]: 60 [0], given: 14 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 09 Oct 2015, 14:30 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 I found an almost identical question with the same question stem, but different statements. Here it is: if-x-y-and-z-are-integers-greater-than-1-and-90644.html Manager Joined: 12 Sep 2015 Posts: 113 GMAT 1: Q V Followers: 0 Kudos [?]: 7 [0], given: 24 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 07 Feb 2016, 10:19 There is one thing I don't understand about this problem and would appreciate any help. When we simplify the equation and get 5^2 * (z) = 3 * (x^y), why do we even need any of the statements in the first place? Why isn't it directly clear that z is 3, x is 5 and y is 2? I really don't get it. Thank you so much in advance. Jay Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2134 Kudos [?]: 13653 [0], given: 222 Re: If x, y, and z are integers greater than 1, and (3^27)(35^10 [#permalink] ### Show Tags 08 Apr 2016, 21:31 MrSobe17 wrote: There is one thing I don't understand about this problem and would appreciate any help. When we simplify the equation and get 5^2 * (z) = 3 * (x^y), why do we even need any of the statements in the first place? Why isn't it directly clear that z is 3, x is 5 and y is 2? I really don't get it. Thank you so much in advance. Jay z can take any value in that case. Think of a case in which z = 12. $$5^2 * 3 * 2^2 = 3 * x^y$$ Here x = 10 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Re: If x, y, and z are integers greater than 1, and (3^27)(35^10   [#permalink] 08 Apr 2016, 21:31
Similar topics Replies Last post
Similar
Topics:
2 If z and x are integers with absolute values greater than 1, is z^x 3 09 Feb 2016, 08:54
4 If x, y, and z are integers greater than 0 and x = y + z 8 11 Nov 2010, 01:55
3 Integers X, Y and Z are greater than zero. Is X percent of Y 8 01 Nov 2010, 14:55
51 If x, y, and z are integers greater than 1, and 31 21 Feb 2010, 13:20
21 If integers x, y and z are greater than 1 what is the value 22 04 Aug 2008, 10:05
Display posts from previous: Sort by