• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 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 2 expert replies and 0 member replies

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

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
497 members
Upvotes:
2867
GMAT Score:
800
Post
Hi LUANDATO,

While this question might look 'scary', it can be solved rather easily by TESTing VALUES.

Since B appears on both sides of the equation, we'll TEST a value for B and then solve for Y....

IF...
B = 0
(9^Y) + (3^0) = (10)(3^0)
(9^Y) + 1 = (10)(1)
(9^Y) = 9
Y = 1

The question asks for the value of 2Y, so we're looking for an answer that equals 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
Quote:
$$If\ \ 9^y+3^b=10*3^b,\ \ then\ \ 2y=?$$

(A) b-2
(B) b-1
(C) b
(D) b+1
(E) b+2

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Hi LUANDATO,
Lets take a look at your question.

$$9^y+3^b=10\times3^b$$
$$\left(3^2\right)^y+3^b=10\times3^b$$
$$\left(3^2\right)^y=10\times3^b-3^b$$
$$3^{2y}=10\times3^b-3^b$$
$$3^{2y}=3^b\left(10-1\right)$$
$$3^{2y}=3^b\left(9\right)$$
$$3^{2y}=3^b\left(3^2\right)$$
$$3^{2y}=3^{b+2}$$
Since bases are equivalent, therefore, exponents will be equal as well,
$$2y=b+2$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any followup.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 32 first replies
5 GMATGuruNY 26 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 Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

60 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

37 posts
See More Top Beat The GMAT Experts