• Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free

    Available with Beat the GMAT members only code

    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam

    Available with Beat the GMAT members only code

    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

    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    Veritas Prep


This topic has 3 expert replies and 0 member replies
kamalakarthi Senior | Next Rank: 100 Posts Default Avatar
31 Jan 2011
80 messages
Followed by:
2 members


Post Mon Jul 24, 2017 6:49 pm
Elapsed Time: 00:00
    Hi, I would like to know if there is better approach to this question instead of solving for equations. Can you please help.

    This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

    GMAT/MBA Expert

    Ian Stewart GMAT Instructor
    02 Jun 2008
    2285 messages
    Followed by:
    344 members
    1090 times
    GMAT Score:
    Post Mon Jul 24, 2017 8:45 pm
    If (a, 4) and (a, b+1) are on the same line, and that line isn't vertical, they must be the same point, because they have the same x-coordinate. So b+1 = 4, and b = 3. We know (4, b) is on the line, so if b = 3, the point (4, 3) is on the line. That means the point must work in the line's equation:

    y = kx + 1

    Plugging in x = 4 and y = 3, we have

    3 = 4k + 1
    k = 1/2

    There's a way to do this without using as much algebra, but you need to understand slopes well. If a line has this equation:

    y = kx + 1

    then its y-intercept is 1, so the point (0, 1) is on the line. When we find that (4, 3) is also on the line, we know that when we move across 4 units, from x=0 to x=4, the line rises by 2 units, from y=1 to y=3. Since slope = rise/run, slope = 2/4 = 1/2. Since k is the slope of the line, that's the answer. Or once you have the two points, you could just use the slope formula.

    All that said, the answer choices are bizarre. A GMAT question would never include "1 and 1/2" as an answer choice to a slope question; they would always write "5/2". What is the source?

    If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

    Post Tue Jul 25, 2017 6:10 am
    In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 4), and (a, b +1) are three points on the line, where a and b are unknown, then k = ?

    a) 1/2
    b) 1
    c) 1 1/2
    d) 2
    e) 2 1/2

    There's a HUGE CLUE in the fact that (a, 4) and (a, b+1) are both on the same line. Notice that the x-coordinates are the same. If the x-coordinates are the same, then there are two possible scenarios:
    scenario #1: The points (a, 4) and (a, b+1) are DIFFERENT points, in which case the line is vertical (with undefined slope)
    scenario #2: The points (a, 4) and (a, b+1) define the SAME point

    IMPORTANT: If a line is defined by y = kx + 1, then k represents the slope. So, the question is really asking us to find the slope of the line.

    In scenario #1, the slope would be undefined. Since none of the answer choices are undefined, we can rule out scenario #1, which means (a, 4) and (a, b+1) define the SAME point. So, we can be certain that b+1 = 4, which means b = 3

    Now that we know that b = 3, we can use the fact that the point (4,b) is on the line.
    This means that the point (4,3) is on the line y = kx + 1.
    When we plug x=4 and y=3 into the equation, we get 3 = (k)(4) + 1
    Solve to get k = 1/2

    Answer: A


    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!

    GMAT/MBA Expert

    Post Sun Aug 06, 2017 10:41 pm
    Equations are the best way here, but we could always go for another set of them from the ones given above.

    k = the slope of the line, and since k = 0 isn't an option in the answers, know the line ISN'T horizontal. We also know that k is defined, so the line can't be perfectly vertical either.

    Since the line isn't horizontal or vertical, we can't have two points with the same x or y-coordinate on the line. (a, 4) and (a, b + 1) have the same x-coordinate, and we just saw that they can't be different points, so they must be the SAME POINT, and 4 = b + 1.

    That gives b = 3, from which we know that (4, 3) and (a, 4) are two points on the line.

    Plugging (4, 3) into the equation y = kx + 1 gives us 3 = 4k + 1, or k = 1/2.

    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!

    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...


    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