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) y is prime
(2) x is prime
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Integer
This topic has expert replies
-
theCodeToGMAT
- Legendary Member
- Posts: 1556
- Joined: Tue Aug 14, 2012 11:18 pm
- Thanked: 448 times
- Followed by:34 members
- GMAT Score:650
To find --> xvinay1983 wrote:If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?
(1) y is prime
(2) x is prime
327 * 510 * z / 58 * 914 * y = x
327 = 3 * 109
510 = 2 * 5 * 3 * 17
58 = 2 * 29
914 = 2 * 457
(3 * 109) * (5 * 3 * 17) * Z
________________________ = X
2 * 29 * 457 * y
Statement 1:
y is prime
X can have any value
INSUFFICIENT
Statement 2:
X is prime
y can have any value .. subsequently.. X can have any value out of 109,3,5,17
INSUFFICIENT
Combining...
y = 3 (Out of 109, 5, 3, 17)
Z = 457 * 29 * 2
x = NOT PRIME
I got stuck here...... What is the OA????
R A H U L
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
I believe that the problem should read as follows:
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²)¹�(x^y)
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²�)(x^y)
(5²)(z) = (3)(x^y)
z = (3) * (x^y)/5².
Since z is an INTEGER, the resulting equation implies that z is a multiple of 3 and that x^y is a multiple of 5².
Statement 1: z is prime
Since z is prime and a multiple of 3, z=3.
Thus, (x^y)/5² = 1, implying that x=5 and y=2.
SUFFICIENT.
Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y≥2.
SUFFICIENT.
The correct answer is D.
(3²�)(35¹�)(z) = (5�)(7¹�)(9¹�)(x^y)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
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²)¹�(x^y)
(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²�)(x^y)
(5²)(z) = (3)(x^y)
z = (3) * (x^y)/5².
Since z is an INTEGER, the resulting equation implies that z is a multiple of 3 and that x^y is a multiple of 5².
Statement 1: z is prime
Since z is prime and a multiple of 3, z=3.
Thus, (x^y)/5² = 1, implying that x=5 and y=2.
SUFFICIENT.
Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y≥2.
SUFFICIENT.
The correct answer is D.
Last edited by GMATGuruNY on Tue Oct 08, 2013 4:54 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
vinay1983
- Legendary Member
- Posts: 643
- Joined: Wed Aug 14, 2013 4:27 am
- Thanked: 48 times
- Followed by:7 members
Sorry. I am a little out of ordertheCodeToGMAT wrote:To find --> xvinay1983 wrote:If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?
(1) y is prime
(2) x is prime
327 * 510 * z / 58 * 914 * y = x
327 = 3 * 109
510 = 2 * 5 * 3 * 17
58 = 2 * 29
914 = 2 * 457
(3 * 109) * (5 * 3 * 17) * Z
________________________ = X
2 * 29 * 457 * y
Statement 1:
y is prime
X can have any value
INSUFFICIENT
Statement 2:
X is prime
y can have any value .. subsequently.. X can have any value out of 109,3,5,17
INSUFFICIENT
Combining...
y = 3 (Out of 109, 5, 3, 17)
Z = 457 * 29 * 2
x = NOT PRIME
I got stuck here...... What is the OA????
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
GMAT/MBA Expert
-
lunarpower
- GMAT Instructor
- Posts: 3380
- Joined: Mon Mar 03, 2008 1:20 am
- Thanked: 2256 times
- Followed by:1535 members
- GMAT Score:800
A student pointed me to Mitch's solution on this thread, in particular the part about statement 2.
Mitch --
However, I was wondering how you arrived at y = 2. For instance, why can't y = 3, in which case z = 15? Or y = 4, in which case z = 45? Etc. After all, we are no longer constrained by the requirement that z be prime.
Mitch --
It's true that x has to be 5. (Since we only care about x, this is all that matters for the problem at hand.)GMATGuruNY wrote:Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y=2.
SUFFICIENT.
However, I was wondering how you arrived at y = 2. For instance, why can't y = 3, in which case z = 15? Or y = 4, in which case z = 45? Etc. After all, we are no longer constrained by the requirement that z be prime.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Pesky typos! The solution should have indicated that y≥2 (since x^y must be a multiple of 5² and x must be prime). Edited my reply.lunarpower wrote:However, I was wondering how you arrived at y = 2. For instance, why can't y = 3, in which case z = 15? Or y = 4, in which case z = 45? Etc. After all, we are no longer constrained by the requirement that z be prime.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
