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OG16 - PS 162

This topic has 3 expert replies and 0 member replies
amina.shaikh309 Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Apr 2016
Posted:
31 messages

OG16 - PS 162

Post Thu May 26, 2016 5:56 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])

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    Post Thu May 26, 2016 6:01 am
    Quote:
    At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had ESTIMATED for the job, in hours?

    28
    24
    16
    14
    12
    Here's an algebraic solution:

    Let h = # of hours that Don ESTIMATED for the job.
    So, h + 4 = ACTUAL # of hours it took Don to complete the job.

    So, IF Don, had completed the job in h hours, his RATE would have = $336/h
    However, since Don completed the job in h+4 hours, his RATE was actually = $336/(h + 4)

    ...consequently, he earned 2$ per hour less than his regular hourly rate.
    In other words, (John's estimated rate) - 2 = (John's actual rate)
    So, $336/h - 2 = $336/(h + 4)

    ASIDE: since the above equation is a bit of a pain to solve, you might consider plugging in the answer choices to see which one works.

    Okay, let's solve this: $336/h - 2 = $336/(h + 4)
    To eliminate the fractions, multiply both sides by (h)(h+4) to get: 336(h+4) - 2(h)(h+4) = 336h
    Expand: 336h + 1344 - 2h² - 8h = 336h
    Simplify: -2h² - 8h + 1344 = 0
    Multiply both sides by -1 to get: 2h² + 8h - 1344 = 0
    Divide both sides by 2 to get: h² + 4h - 672 = 0
    Factor (yeeesh!) to get: (h - 24)(h + 28) = 0
    Solve to get: h = 24 or h = -28
    Since h cannot be negative (in the real world), h must equal 24.

    Answer: B

    Cheers,
    Brent

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    Post Thu May 26, 2016 8:09 am
    Quote:
    At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

    28
    24
    16
    14
    12
    We can PLUG IN THE ANSWERS, which represent the estimated time: 28, 24, 16, 14, or 12.
    The actual time was 4 hours longer: 32, 28, 20, 18, or 16.
    Both the estimated time and the actual time must divide evenly into 336 (the labor cost).
    Since 336 is not a multiple of 32, eliminate A.
    Since 336 is not a multiple of 20, eliminate C.
    336 is not a multiple of 9, since the sum of its digits is not a multiple of 9.
    Thus, 336 is not a multiple of 18; eliminate D.

    The correct answer must be B or E.

    Answer choice B: estimated time = 24, actual time = 28
    Estimated payrate = 336/24 = 14.
    Actual payrate = 336/28 = 12.
    Difference = 14-12 = 2.
    Success!

    The correct answer is B.

    Note that we had to try only ONE answer choice -- a very efficient way to solve the problem.

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    GMAT/MBA Expert

    Post Thu May 26, 2016 2:49 pm
    If we've got

    336 = x * y

    and

    336 = (x + 4) * (y - 2)

    We could factor 336 to look for solutions. Since the answers are likely to have both the time and the hourly rate (in an attempt to trap us if we're not careful), we might cheat with them and assume that they multiply to our number ... which, of course, they do!

    336 = 28 * 12
    336 = 24 * 14

    Since Don's estimate had a lower time and a higher hourly rate, his estimate must've been 24 * 14. We want the time, which must be LOWER than the time in the other equation, so our answer is 24.

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