• 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
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Lots of exponents

This topic has 2 expert replies and 0 member replies
JJMforthegold Newbie | Next Rank: 10 Posts Default Avatar
Joined
29 Aug 2017
Posted:
5 messages

Lots of exponents

Post Sun Sep 17, 2017 3:45 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Experts-

    Is there a fast way solve this without multiplying everything out?

    (0.0015 x 10^m)/(0.03 x 10^k) = 5 x 10^7, then m - k =

    a) 9
    b) 8
    c) 7
    d) 6
    e) 5
    a

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Sep 17, 2017 4:24 pm
    Quote:
    if (0.0015 x 10^m) / (0.03 x 10^k) = 5 x 10^7, then m - k = ?

    a. 9
    b. 8
    c. 7
    d. 6
    e. 5
    Here's one approach:

    First rewrite the equation as:
    (0.0015/0.03) x (10^m)/(10^k) = 5 x 10^7
    Simplify to get: (0.0015/0.03) x 10^(m-k) = 5 x 10^7

    Aside: A quick way to simplify 0.0015/0.03 is to multiply top and bottom by 10,000 to get 15/300.
    Simplify to get 1/20

    So, we now have (1/20) x 10^(m-k) = 5 x 10^7
    Isolate 10^(m-k) by multiplying both sides by 20 to get:
    10^(m-k) = (20)(5) (10^7)
    Simplify: 10^(m-k) = (100)(10^7)
    Simplify: 10^(m-k) = (10^2)(10^7)
    Simplify: 10^(m-k) = 10^9

    So, m-k must equal 9

    Answer: A

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Sun Sep 17, 2017 6:15 pm
    JJMforthegold wrote:
    Experts-

    Is there a fast way solve this without multiplying everything out?

    (0.0015 x 10^m)/(0.03 x 10^k) = 5 x 10^7, then m - k =

    a) 9
    b) 8
    c) 7
    d) 6
    e) 5
    Let k=0.
    (0.0015 * 10^m) / (0.03* 10^0) = (5 * 10^7)

    Convert the decimals to integers:
    (15 * 10^(-4) * 10^m / (3 * 10^(-2) * 1) = (5 * 10^7)

    Divide the integers and subtract the exponents:
    5 * 10^(-2) * 10^m = 5 * 10^7

    Cancel the 5's and divide each side by 10^(-2):
    10^m = 10^9
    m = 9.

    Thus:
    m-k = 9-0 = 9.

    The correct answer is A.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    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.

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts