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A merchant paid $300 for a shipment of x identical calculato

This topic has 2 expert replies and 0 member replies

A merchant paid $300 for a shipment of x identical calculato

Post Sat Sep 16, 2017 4:53 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

    A. 24
    B. 25
    C. 26
    D. 28
    E. 30

    Is there a strategic approach to this question?

    OA: E

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    Post Sat Sep 16, 2017 6:18 am
    ardz24 wrote:
    A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?

    A. 24
    B. 25
    C. 26
    D. 28
    E. 30

    Here's one approach:

    If it costs $300 to purchase x calculators, then the average cost per calculator is 300/x

    Later, the calculators are sold for $5 more than the average purchase cost of 300/x dollars
    So, the resell price is 300/x + 5

    How many were sold? Well, the merchant began with x calculators, but used 2 as demonstrators, so the merchant sold x - 2 calculators.

    Finally, the merchant's profit was $120 (after a $300 investment). So, the revenue was $420

    We can now write an equation: (300/x + 5)(x - 2) = 420

    IMPORTANT: This is an awful equation to solve. At this point, it may be faster to try plugging in the answer choices.

    Or we can solve the equation.
    (300/x + 5)(x - 2) = 420
    Expand: 300 - (600/x) + 5x - 10 = 420
    Multiply both sides by x: 300x - 600 + 5x^2 - 10x = 420x
    Simplify: 5x^2 - 130x - 600 = 0
    Divide both sides by 5: x^2 - 26x - 120 = 0
    Factor: (x - 30)(x + 4) = 0
    So, x = 30 or x = -4

    Since x can't be negative, x = 30 = E

    Cheers,
    Brent

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    Post Tue Sep 19, 2017 2:53 pm
    Hi ardz24,

    The information in the prompt include a variety of nice 'round' numbers, so it's likely that the number of calculators in the shipment is also a round number AND divides evenly into 300. Only two of the answers 'fit' that idea - 25 and 30, so let's TEST THE ANSWERS and see if either of those values fits all of the information given in the prompt.

    IF.... X = 30 and there are 30 calculators in the shipment....
    The merchant paid $300/30 = $10 per calculator
    2 calculators were used for demonstrations, so 30 - 2 = 28 calculators were sold
    Each of the 'sold' calculators brought in $10+$5 = $15
    The total revenue was ($15)(28) = $420
    The total profit was $420 - $300 = $120

    This is an exact match for what we were told, so this MUST be the answer.

    Final Answer: E

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: ardz24

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