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PS - Rate & Times

This topic has 3 expert replies and 3 member replies
bml1105 Master | Next Rank: 500 Posts
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PS - Rate & Times

Post Sun May 04, 2014 5:23 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

      (A) 11x/y
      (B) 11y/x
      (C) x/11y
      (D) 11/xy
      (E) xy/11


    Correct Answer: A

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    Post Sun May 04, 2014 5:35 pm
    bml1105 wrote:
    If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

      (A) 11x/y
      (B) 11y/x
      (C) x/11y
      (D) 11/xy
      (E) xy/11


    One option is to use equivalent ratios.
    The ratio is time/distance

    For every 11 seconds, Juan can run y yards
    So we get the ratio 11/y

    Let T = the time it takes to run x yards.
    That is, For every T seconds, Juan can run x yards
    We get the ratio T/x

    Since Juan runs at a constant rate, we can write: we get: 11/y = T/x
    Cross multiply to get: 11x = Ty
    Divide both sides by y to get: 11x/y = T
    So, the answer is A

    Cheers,
    Brent

    _________________
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    Post Sun May 04, 2014 5:40 pm
    bml1105 wrote:
    If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

      (A) 11x/y
      (B) 11y/x
      (C) x/11y
      (D) 11/xy
      (E) xy/11

    Another approach is to use the various speed-distance-time formulas.

    Juan takes 11 seconds to run y yards
    Speed = distance/time
    So, Juan's speed= y/11 yards per second

    How many seconds will it take him to run x yards at the same rate
    Time = distance/speed
    So, Time = x/(y/11)
    = 11x/y
    = 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

    Thanked by: Reyad2016
    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 May 04, 2014 5:49 pm
    bml1105 wrote:
    If Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

      (A) 11x/y
      (B) 11y/x
      (C) x/11y
      (D) 11/xy
      (E) xy/11


    We can also solve the question using the input-output approach.
    For example, let's let y = 22
    This means that Juan takes 11 seconds to run 22 yards, which means his speed is 2 yards per second.

    From here, if we let x = 10, then the question is asking,"how many seconds will it take Juan to run 10 yards at the same rate (of 2 yards per second)?"
    Well, at that speed, it will take Juan 5 seconds to run 10 yards.

    In other words, if we INPUT y = 22 and x = 10, then the answer (the OUTPUT) to the question is 5.

    Now we'll plug y = 22 and x = 10 into the answer choices and see which one yields the OUTPUT of 5
    (A) 11x/y = (11)(10)/22 = 5 GREAT!
    (B) 11y/x = (11)(22)/10 = something other than 5 ELIMINATE B
    (C) x/11y = (10)/(11)(22) = something other than 5 ELIMINATE C
    (D) 11/xy (11)/(10)(22) = 1/20 ELIMINATE D
    (E) xy/11 = (10)(22)/(11) = 20 ELIMINATE E

    A is the only answer that works.

    Cheers,
    Brent[/spoiler]

    _________________
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    Come see all of our free resources

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    bml1105 Master | Next Rank: 500 Posts
    Joined
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    Posted:
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    Post Sun May 04, 2014 6:25 pm
    I was using the formula of Rate X Time = Distance

    Rate = 11/y
    Time = what we're trying to find
    Distance = x

    x/(11/y) = x(y/11) = xy/11

    How come that doesn't work?

    Post Sun May 04, 2014 7:35 pm
    Hi bml1105,

    There's one small mistake in your approach:

    To use the Distance Formula, the Rate has to be in the form "distance/time" (e.g.. miles per hour).

    In this prompt, the rate is inverted (it states "11 seconds to run Y yards"; that's "time/distance")

    Converting the rate to the correct format gives us….

    Rate = Y/11
    Distance = X
    Time = T

    D = R(T)

    X = (Y/11)T

    X/(Y/11) = T

    11X/Y = T

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    bml1105 Master | Next Rank: 500 Posts
    Joined
    24 Nov 2013
    Posted:
    113 messages
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    5 members
    Thanked:
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    Post Mon May 05, 2014 6:16 am
    Thanks Rich! I woke up this morning and realized what I had done wrong. Dreaming about GMAT problems cannot be a good sign!

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