Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55635

For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
21 Feb 2017, 05:17
Question Stats:
52% (01:36) correct 48% (01:57) wrong based on 241 sessions
HideShow timer Statistics
For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y? A. 12 B. 3 C. 0 D. 9 E. Cannot be determined
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
21 Feb 2017, 05:43
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined 3^(4x+12)=5^(3x+y) This relation will hold true if the power of 3 and 5 on both sides of equation become zero because \({anything}^0 = 1\)i.e. 4x+12 = 0 and 3x+y=0 i.e. x = 2 and y = 9 Answer: Option D
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




CEO
Joined: 12 Sep 2015
Posts: 3777
Location: Canada

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
22 Feb 2017, 08:34
Bunuel wrote: For integers x and y, 3^(4x+12) = 5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined The key word in this question is INTEGERS Notice that, if x is an integer, then 4x+12 is an integer, which means 3^(4x+12) will equal the product of a bunch of 3's Likewise, if x and y are integers, then 3x+y is an integer, which means 5^(3x+y) will equal the product of a bunch of 5's Given these conditions, it seems impossible that 3^(4x+12) could ever equal 5^(3x+y) HOWEVER, if the exponents 4x+12 and 3x + y both equal ZERO, then we get 3^0 and 5^0, and both of these evaluate to equal 1  PERFECT! So, let 4x+12 = 0 and let 3x+y = 0 Now we'll solve this system of equations for x and y. First, if 4x+12 = 0, then x = 3 If x = 3, then we can take 3x+y = 0 and replace x with 3 to get: 3(3) + y = 0 Simplify: 9 + y = 0 Solve: y = 9 So, x = 3 and y = 9, is a solution to the equation 3^(4x+12) = 5^(3x+y) Answer: D Cheers, Brent
_________________
Test confidently with gmatprepnow.com



CEO
Joined: 12 Sep 2015
Posts: 3777
Location: Canada

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
22 Feb 2017, 08:35
GMATinsight wrote: i.e. 4x+12 = 0 and 3x+y=0 i.e. x = 2 and y = 9
Answer: Option D
Small error with the xvalue above. Should be x = 3 Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
23 Feb 2017, 10:45
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined In order for the two sides of the equation to be equal, the exponent (4x+12) must equal zero and the exponent (3x+y) must equal zero, since 3^0 = 1 and 5^0 = 1. Thus: 4x + 12 = 0 4x = 12 x = 3 and 3x + y = 0 y = 3x Since x = 3, y = 3(3) = 9. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Retired Moderator
Joined: 19 Mar 2014
Posts: 929
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
17 Jul 2017, 06:10
GMATinsight wrote: Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined 3^(4x+12)=5^(3x+y) This relation will hold true if the power of 3 and 5 on both sides of equation become zero because \({anything}^0 = 1\)i.e. 4x+12 = 0 and 3x+y=0 i.e. x = 2 and y = 9 Answer: Option D Hello GMATinsight  You solution is really the quickest way to do! Somehow I spent 4 mins to solve this. Just one correction, the value you mentioned for x is incorrect, x should be 3
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475



Retired Moderator
Joined: 19 Mar 2014
Posts: 929
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
17 Jul 2017, 06:14
For integers x and y, \(3^{4x+12}=5^{3x+y}\). What is the value of y?\(3^{4x+12}=5^{3x+y}\) This is only possible when both 3 and 5 are raised to the power of ZERO. 4x + 12 = 0 3x + y = 0 Solving these two equations we get: \(x = 3\) \(y = 9\) Hence, Answer is DDid you like the answer? 1 Kudos Please
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
18 Aug 2018, 18:25
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined Since 3^(4x+12) = 5^(3x+y) and 3 and 5 are relatively prime to each other (that is, they don’t have a common factor other than 1), the only way those two expressions can be equal is if each base is raised to the zero power and thus each side is equal to 1. Thus: 4x + 12 = 0 4x = 12 x = 3 Substituting, we have: 3(3) + y = 0 9 + y = 0 y = 9 Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



VP
Joined: 09 Mar 2018
Posts: 1004
Location: India

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
04 Feb 2019, 23:02
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined Had thought of an approach, but still forgot to consider this5^0 * 3^( 4x+12)=5^(3x+y) 3^0 3x +y = 0 & 4x+12 = 0, x =3 y = 3*3 = 9 D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.



Manager
Joined: 22 Sep 2018
Posts: 249

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
05 Feb 2019, 16:20
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined My reasoning: In order for these two values to be equal each other \(3^{(4x+12}) and 5^{(3x+y)}\) must BOTH be equal to 1. The reason is because 5 raised to any power will never equal 3 raised to any power unless they are both raised to the power of 0. Explained even further: \(5^3\) = 5*5*5. Notice how there are no 3s in the prime factorization. So we can set 4x+12 = 0 and see that x = 3. If x =3, y must equal 9



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6522
Location: United States (CA)

Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
Show Tags
06 Feb 2019, 20:51
Bunuel wrote: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y?
A. 12 B. 3 C. 0 D. 9 E. Cannot be determined In order for a power in base 3 to equal a power in base 5, the exponents of each base must equal zero. In other words, 3^0 = 1 and 5^0 = 1, and so 3^0 = 5^0. This is the only way that the original equation can be satisfied. Thus, since each exponent must equal 0, we have: 4x + 12 = 0 4x = 12 x = 3 Solving for y, we have: 3(3) + y = 0 9 + y = 0 y = 9 Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y?
[#permalink]
06 Feb 2019, 20:51






