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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

clock problem...How to think and solve

This topic has 1 expert reply and 1 member reply

Top Member

clock problem...How to think and solve

Post Wed Sep 20, 2017 9:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    At exactly what time past 7:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time ?

    (A) 20 13/21 minutes past 7:00
    (B) 20 13/17 minutes past 7:00
    (C) 21 3/23 minutes past 7:00
    (D) 21 9/11 minutes past 7:00
    (E) 22 4/9 minutes past 7:00

    Source: 800 Score
    OA: D



    Last edited by Mo2men on Wed Sep 20, 2017 10:32 am; edited 1 time in total

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Sep 20, 2017 10:10 am
    Hi Mo2men,

    To start, given the correct answer, the 5 answer choices should be ordered from 'least' to 'greatest', meaning that they should be:

    a) 20 13/21 minutes past 7:00
    b) 20 13/17 minutes past 7:00
    c) 21 3/23 minutes past 7:00
    d) 21 9/11 minutes past 7:00
    e) 22 4/9 minutes past 7:00

    When dealing with a clock face, there are several pieces of information to consider:
    1) A clock face is 360 degrees, so each "hour mark" represents 30 degrees and each "minute mark" represents 6 degrees.
    2) As the minute hand moves, the hour hand ALSO moves (a little). Over the course of 1 full hour of time, the minute hand will move 360 degrees and the hour hand will move 30 degrees.
    3) For each MINUTE that the minute hand moves, the hour hand moves 0.5 DEGREES.

    To find the first time AFTER 7:00 that the hour hand and minute hand are PERPENDICULAR (meaning that their positions are 90 degrees apart), you might find it useful to work in small increments. From the answer choices, we see that the correct answer has to be fairly close to 7:20, so we'll 'work up' to there:

    At 7:00...
    the minute hand is at 0 degrees
    the hour hand is at 210 degrees

    At 7:20...
    the minute hand is at 120 degrees
    the hour hand has moved to 210 + 10 = 220 degrees
    So the arms are getting closer to where we want them to be, but they're not there yet (they're 100 degrees apart)...

    At 7:21...
    the minute hand is at 126 degrees
    the hour hand has moved to 220 + 0.5 = 220.5 degrees
    So the arms are getting closer to where we want them to be, but they're not there yet (now they're 94.5 degrees apart)...

    At 7:22...
    the minute hand is at 132 degrees
    the hour hand has moved to 220.5 + 0.5 = 221 degrees
    Here, the minute hand has 'overshot' just a little bit (now they're 89 degrees apart)... Thus, the correct answer has to be just a little 'earlier' than 7:22

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: Mo2men

    Top Member

    Post Wed Sep 20, 2017 10:26 am
    Rich.C@EMPOWERgmat.com wrote:
    Hi Mo2men,

    To start, given the correct answer, the 5 answer choices should be ordered from 'least' to 'greatest', meaning that they should be:

    a) 20 13/21 minutes past 7:00
    b) 20 13/17 minutes past 7:00
    c) 21 3/23 minutes past 7:00
    d) 21 9/11 minutes past 7:00
    e) 22 4/9 minutes past 7:00

    When dealing with a clock face, there are several pieces of information to consider:
    1) A clock face is 360 degrees, so each "hour mark" represents 30 degrees and each "minute mark" represents 6 degrees.
    2) As the minute hand moves, the hour hand ALSO moves (a little). Over the course of 1 full hour of time, the minute hand will move 360 degrees and the hour hand will move 30 degrees.
    3) For each MINUTE that the minute hand moves, the hour hand moves 0.5 DEGREES.

    To find the first time AFTER 7:00 that the hour hand and minute hand are PERPENDICULAR (meaning that their positions are 90 degrees apart), you might find it useful to work in small increments. From the answer choices, we see that the correct answer has to be fairly close to 7:20, so we'll 'work up' to there:

    At 7:00...
    the minute hand is at 0 degrees
    the hour hand is at 210 degrees

    At 7:20...
    the minute hand is at 120 degrees
    the hour hand has moved to 210 + 10 = 220 degrees
    So the arms are getting closer to where we want them to be, but they're not there yet (they're 100 degrees apart)...

    At 7:21...
    the minute hand is at 126 degrees
    the hour hand has moved to 220 + 0.5 = 220.5 degrees
    So the arms are getting closer to where we want them to be, but they're not there yet (now they're 94.5 degrees apart)...

    At 7:22...
    the minute hand is at 132 degrees
    the hour hand has moved to 220.5 + 0.5 = 221 degrees
    Here, the minute hand has 'overshot' just a little bit (now they're 89 degrees apart)... Thus, the correct answer has to be just a little 'earlier' than 7:22

    Final Answer: D

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

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 ardz24 40 topics
    5 LUANDATO 32 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    141 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    107 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    106 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    104 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts