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On a certain nonstop trip, Marta averaged

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

On a certain nonstop trip, Marta averaged

Post Tue Aug 08, 2017 7:35 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

    (1) 2x + 3y = 280
    (2) y = x + 10

    Official Guide question
    Answer: A

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    Post Wed Aug 09, 2017 10:48 am
    jjjinapinch wrote:
    On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

    (1) 2x + 3y = 280
    (2) y = x + 10

    Official Guide question
    Answer: A
    Given: Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours

    Target question: What was Marta's average speed for the entire trip?
    This is a good candidate for rephrasing the target question.
    Average speed = (TOTAL distance)/(TOTAL time)
    Travelling at x miles per hour for 2 hours, Marta travels a distance of 2x miles
    Travelling at y miles per hour for 3 hours, Marta travels a distance of 3y miles
    So, the TOTAL distance = 2x + 3y
    TOTAL time = 2 hours + 3 hours = 5 hours
    So, average speed = (2x + 3y)/5
    REPHRASED target question: What is the value of (2x + 3y)/5?

    Statement 1: 2x + 3y = 280
    Perfect!
    This means, (2x + 3y)/5 = 280/5 =56
    Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

    Statement 2: y = x + 10
    There are several values of x and y that satisfy statement 2. Here are two:
    Case a: x = 10 and y = 20. In this case, (2x + 3y)/5 = (20 + 60)/5 = 80/5 =16
    Case b: x = 30 and y = 40. In this case, (2x + 3y)/5 = (60 + 120)/5 = 180/5 =36
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Answer: A

    Cheers,
    Brent

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