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A company makes and sells two products, P and Q.

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mensanumber Junior | Next Rank: 30 Posts Default Avatar
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A company makes and sells two products, P and Q.

Post Sat Dec 12, 2015 12:57 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

    (1) During the month, more units of P than units of Q were sold.
    (2) During the month, at least 100 units of Q were sold.

    I am usually able to solve these questions but just need to spend a lot of time more than 4 mins sometimes. I get confounded in a lot calculations and then handling the implied inequalities involved in such questions. Any tips to solve them in less than 2.5 mins?

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    Post Sun Dec 13, 2015 3:49 am
    mensanumber wrote:
    A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000?

    (1) During the month, more units of P than units of Q were sold.
    (2) During the month, at least 100 units of Q were sold.
    Profit for each unit of P sold = selling price - cost = 10 - 8 = 2.
    Profit for each unit of Q sold = selling price = cost = 13 - 9.5 = 3.5.

    Test EXTREMES.

    Statement 1:
    Case 1: 434 units of P and 400 units of Q are sold
    Total profit = (2)(434) + (3.5)(400) = 868 + 1400 = more than 2000.

    To save time, test an extreme case that still satisfies statement 2.
    Case 2: 734 units of P and 100 units of Q are sold
    Total profit = (2)(734) + (3.5)(100) = 1468 + 350 = less than 2000.

    Case 1 satisfies BOTH statements and yields an answer of YES.
    Case 2 satisfies BOTH statements and yields an answer of NO.

    The correct answer is E.

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    Thanked by: mensanumber
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    mensanumber Junior | Next Rank: 30 Posts Default Avatar
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    Post Mon Dec 14, 2015 10:56 pm
    Thanks for your reply @GMATGuruNY. I followed the exact same steps except for in st1 instead of "Total profit = (2)(434) + (3.5)(400) = 868 + 1400 = more than 2000." I considered "(2)(418) + (3.5)(416)" and wasted a lot of time in calculations.

    But my bigger problem is understanding the implied inequality. It takes me sometime to grab the direction of inequalities and then form equations. Its specific to these types of problems involving "word problems+DS+inequality" combo. I think I need more practice. Can you please suggest more similar problems? Thanks again

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