• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If 9^y + 3^b = 10*3^b, then 2y ='

This topic has 4 expert replies and 1 member reply

If 9^y + 3^b = 10*3^b, then 2y ='

Post
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b - 2
(B) b - 1
(C) b
(D) b + 1
(E) b + 2
OA is E
Please Expert, can you help me out with this problem? Thanks

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
121 members
Upvotes:
1153
GMAT Score:
770
Post
Roland2rule wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b - 2
(B) b - 1
(C) b
(D) b + 1
(E) b + 2
OA is E
Please Expert, can you help me out with this problem? Thanks
This could have been depicted a little more cleanly. Let's assume the initial equation is 9^y + 3^b = 10 * (3^b)
Say b = 1. We get 9^y + 3^1 = 10 * (3^1)
9^y = 27

3^(2y) = 3^3
2y = 3. 3 is our target.

When we plug 1 in for b, only E gives us 3.

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Master | Next Rank: 500 Posts Default Avatar
Joined
15 Oct 2009
Posted:
320 messages
Upvotes:
27
Post
Roland2rule wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b - 2
(B) b - 1
(C) b
(D) b + 1
(E) b + 2
OA is E
Please Expert, can you help me out with this problem? Thanks
Or you could factor the thing:

9^y = (3^2)^y = 3^2y

Rewriting: 3^2y + 3^b =10(3^b)

Factor the left side: (3^b)(3^(2y-b) + 1), so

(3^b)(3^(2y-b) + 1) = 10(3^b)

therefore 3^(2y-b)+1 = 10

and 3^(2y-b) = 9

since 3^2 = 9 , 2y - b must equal 2, therefore

2y-b=2 and 2y = b+2, E

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Roland2rule wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b - 2
(B) b - 1
(C) b
(D) b + 1
(E) b + 2
So that all of the terms with exponents have the same base, let b=2.

Plugging b=9 into 9^y + 3^b = 10(3^b), we get:
9^y + 3² = 10(3²)
9^y + 9 = 10*9
9^y + 9 = 90
9^y = 81
y =2, with the result that 2y = 2*2 = 4.

The question stem asks for the value of 2y (4).
Now plug b=2 into the answer choices to see which yields the target value of 4.
Only E works:
b+2 = 2+2 = 4.

The correct answer is E.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
Hi Roland2rule,

TESTing VALUES works perfectly on this question (as Mitch showed in his explanation). Since there are no 'restrictions' on the values of B and Y (and we're dealing with exponents), you can use the simplest value possible for B... B=0

IF... B=0, then we have...
9^Y + 3^0 = (10)(3^0)
9^Y + 1 = 10(1)
9^Y = 9
Y = 1

We're asked for the value of 2Y, so we're looking for an answer that equals 2(1) = 2 when B=0. There's only one answer that matches.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Roland2rule wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b - 2
(B) b - 1
(C) b
(D) b + 1
(E) b + 2
We see that 9^y = (3^2)^y. Simplifying the equation, we have:

3^2y + 3^b = 10(3^b)

3^2y = 10(3^b) - 3^b

Factoring out 3^b from both terms on the right side of the equation yields:

3^2y = 3^b(10 - 1)

3^2y = 3^b(9)

3^2y = 3^b(3^2)

3^2y = 3^(b + 2)

2y = b + 2

Answer: E

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Top First Responders*

1 Brent@GMATPrepNow 69 first replies
2 fskilnik@GMATH 54 first replies
3 Jay@ManhattanReview 48 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

128 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 image description Max@Math Revolution

Math Revolution

92 posts
4 image description Jay@ManhattanReview

Manhattan Review

86 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

78 posts
See More Top Beat The GMAT Experts