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The average wages of a worker during a fortnight...

This topic has 2 expert replies and 0 member replies

The average wages of a worker during a fortnight...

Post Fri Nov 10, 2017 9:48 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The average wages of a worker during a fortnight comprising 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day?

    A. $83
    B. $90
    C. $92
    D. $97
    E. $104

    The OA is D.

    Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Fri Nov 10, 2017 11:18 am
    Hi swerve,

    We're told that the average pay a worker received for 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. We're asked for his wage on the 8th day.

    There are a number of different ways to approach the 'math' in this question. Here's an approach that allows you to avoid a lot of 'step-heavy' math and focus on the 'relationships' between the numbers.

    Since the average pay was $90/day, we can track how much 'below average' or 'above average' the individual days are...
    -For the first 7 days, the average pay was $87/day, thus each of those days was $3 BELOW the average... meaning that we're (7)($3) = $21 'below' in total here.
    -For the last 7 days, the average pay was $92/day, thus each of those days was $2 ABOVE the average... meaning that we're (7)($2) = $14 'above' in total here.

    With those 14 days, we're a total of '$7 below' what the average is supposed to be, so that final day (the 8th day) has to make up for that difference...

    8th day = $90 + $7 = $97

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: swerve
    Post Fri Nov 10, 2017 1:01 pm
    Quote:
    The average wages of a worker during a fortnight comprising 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day?

    A. $83
    B. $90
    C. $92
    D. $97
    E. $104

    The OA is D.

    Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
    Hi Swerve,
    Let's take a look at your question.

    The wages of a worker during a fortnight comprising 15 consecutive working days = $90 per day
    We know that,
    $$Average\ \ =\ \frac{Sum}{Days}$$
    $$Sum\ =\ Average\ \times\ Days$$
    $$Sum\ =\ 90\ \times15\ =\ 1350$$
    Therefore,
    Sum of wages of 15 days = $1350

    Next the question states that During the first 7 days, his average wages was $87 per day.
    Again using the average formula, we will find the sum of wages of first 7 days.
    $$Average\ \ =\ \frac{Sum}{Days}$$
    $$Sum\ =\ Average\ \times\ Days$$
    $$Sum\ =\ 87\ \times7\ =\ 609$$
    Therefore,
    Sum of wages of first 7 days = $609

    Next the question states that he average wages during the last 7 days was $92 per day.
    Again using the average formula, we will find the sum of wages of last 7 days.
    $$Average\ \ =\ \frac{Sum}{Days}$$
    $$Sum\ =\ Average\ \times\ Days$$
    $$Sum\ =\ 92\ \times7\ =\ 644$$
    Therefore,
    Sum of wages of last 7 days = $644

    We need to find the wage on 8th day.
    We know that,
    Sum of wages of first 7 days + Wage on 8th day + Sum of wages of last 7 days = Sum of wages of 15 days
    Plugin in all the known wages we calculated above,
    609 + Wage on 8th day + 644 = 1350
    Wage on 8th day + 609 + 644 = 1350
    Wage on 8th day + 1253 = 1350
    Wage on 8th day = 1350 - 1253
    Wage on 8th day = 97
    The wage on 8th day is $97.

    Therefore, Option D is true.

    Hope it helps.
    I am available if you'd like any follow up.

    _________________
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