It is currently 23 Feb 2018, 00:53

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

Intern
Intern
avatar
Joined: 29 Oct 2013
Posts: 18
If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 31 Aug 2014, 23:15
(3^27)*(5^10)*(z)=(3^28)*(5^8)*(x^y)

z= (3/25)* (x^y)
So x^y should be a multiple of 25 since they're all integers

i. y is prime
This gives us no info about. It could be any integer greater than 1. Insufficient

ii. x is prime
5 is the only prime whose powers are multiples of 25. So the value of y is irrelevant since it is greater than 1. x=5. SUFFICIENT

Answer B
Manager
Manager
avatar
Joined: 24 Jul 2011
Posts: 227
Location: India
GMAT 1: 570 Q50 V19
GMAT 2: 650 Q49 V28
GMAT 3: 690 Q50 V34
WE: Information Technology (Investment Banking)
GMAT ToolKit User Reviews Badge
Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 13 Oct 2015, 07:37
Hi Bunuel,

I agree, over here I am deflecting out of the scope of GMAT.

In one of the similar questions on GMATClub, I found that you used the concept of log and marked answer as E.

"y" can be log something to base x. So equation is independent of x.

Can we see such ambiguity (unless I am wrong in above scenario) on real GMAT exam?
_________________

Middle of nowhere!

Manager
Manager
avatar
B
Joined: 23 Dec 2013
Posts: 235
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Reviews Badge
Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 23 May 2017, 06:57
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.


Rephrased question: 5^2z = 3x^y

Goal: The goal here is to find a unique value of X

Statement 1: Y is prime. We know that x has to be a power of 5 to balance out the 5^2 on the other equation, but we don't know if z has a 5 as a prime factor, making x potentially greater than 25 (=5^2). Since we don't know the size of x because we y is a prime, this info is insufficient.

Statement 2: X is prime. Now we know that x is prime, so it has to be 5. Any other power of 5 will not be prime. You can pick numbers to prove it to yourself. In this case, x =5 to balance out the 5 on the other side of the equation. Sufficient.
Manager
Manager
avatar
S
Joined: 22 Apr 2017
Posts: 113
Location: India
GMAT 1: 690 Q48 V35
GPA: 3.7
GMAT ToolKit User
If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 12 Jan 2018, 22:02
I think there is a typo with the Stem 1. Per the MGMAT, the question is:

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

and the OA is D.

niks18 Pls check
Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 4904
GPA: 3.82
Re: If x, y, and z are integers greater than 1, and [#permalink]

Show Tags

New post 14 Jan 2018, 21:29
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.


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (\(x\), \(y\) and \(z\)) and 1 equations, C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2)
\(3^{27}\cdot 5^{10}\cdot z= 5^8 \cdot 9^{14} \cdot x^y\)
\(⇔5^2\cdot z = 3\cdot x^y\)
\(⇔x=5,y=2,z=3\) since both are prime number factorization.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
\(x=5,y=2,z=3\)
\(x=10,y=2,z=12\)
The condition 1) only is not sufficient.

Condition 2)
\(x = 5 y = 2, z = 3\) since \(x\) is a prime.
After canceling out all corresponding primes from the both sides, we have 5 from the left hand side and so \(x\) must be 5.
The condition 2) only is sufficient.

Therefore, B is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: If x, y, and z are integers greater than 1, and   [#permalink] 14 Jan 2018, 21:29

Go to page   Previous    1   2   [ 25 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®.