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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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

OG The straight-line graphs of the three equations

This topic has 2 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
Joined
02 Jul 2017
Posted:
191 messages
Followed by:
1 members
Thanked:
1 times

OG The straight-line graphs of the three equations

Post Tue Aug 22, 2017 7:41 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    y = ax - 5
    y = x + 6
    y = 3x + b

    In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?

    (1) a = 2
    (2) r = 17

    D

    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

    Post Fri Aug 25, 2017 9:57 am
    AbeNeedsAnswers wrote:
    y = ax - 5
    y = x + 6
    y = 3x + b

    In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?

    (1) a = 2
    (2) r = 17

    D
    We can begin by substituting p and r for x and y, respectively, in the three given equations.

    1) r = ap - 5

    2) r = p + 6

    3) r = 3p + b

    Statement One Alone:

    a = 2

    We can substitute 2 for a in the equation r = ap - 5. Thus, we have:

    r = 2p - 5

    Next we can set equations 1 and 2 equal to each other.

    2p - 5 = p + 6

    p = 11

    Since p = 11, we see that r = 11 + 6 = 17

    Finally, we can substitute 11 for p and 17 for r in equation 3. This gives us:

    17 = 3(11) + b

    17 = 33 + b

    -16 = b

    Statement one alone is sufficient to answer the question.

    Statement Two Alone:

    r = 17

    We can substitute r into all three equations and we have:

    1) 17 = ap - 5

    2) 17 = p + 6

    3) 17 = 3p + b

    We see that p = 11. Now we can substitute 11 for p in equation 3 to determine a value for b.

    17 = 3(11) + b

    -16 = b

    Statement two alone is also sufficient to answer the question.

    Answer: D

    _________________

    Scott Woodbury Stewart Founder & CEO
    GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
    5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

    Post Fri Sep 01, 2017 5:21 pm
    Hi AbeNeedsAnswers,

    We're given the equations for 3 lines (and those equations are based on 4 unknowns: 2 variables and the 2 'constants' A and B):
    Y = (A)(X) - 5
    Y = X + 6
    Y = 3X + B
    We're told that the three lines all cross at one point on a graph (p,r). We're asked for the value of B. While this question looks complex, it's actually built around a 'system' math "shortcut" - meaning that since we have 3 unique equations and 4 unknowns, we just need one more unique equation (with one or more of those unknowns) and we can solve for ALL of the unknowns:

    1) A =2

    With this information, we now have a 4th equation, so we CAN solve for B.
    Fact 1 is SUFFICIENT

    2) R = 17

    This information tell us the x co-ordinate where all three lines will meet, so it's the equivalent of having X=17 to work with. This 4th equation also allows us to solve for B.
    Fact 2 is SUFFICIENT

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 LUANDATO 44 topics
    5 ardz24 40 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

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

    EMPOWERgmat

    110 posts
    3 image description EconomistGMATTutor

    The Economist GMAT Tutor

    109 posts
    4 image description GMATGuruNY

    The Princeton Review Teacher

    107 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    72 posts
    See More Top Beat The GMAT Experts