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

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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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by GMATGuruNY » Sun Dec 13, 2015 3:49 am

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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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by mensanumber » Mon Dec 14, 2015 10:56 pm

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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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mensanumber wrote:
Sat Dec 12, 2015 12:57 pm
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.
We see that product P has a profit of $2 per unit and product Q has a profit of $3.50 per unit. If we let p = the number of units of product P sold and q = the number of units of product Q sold, we can create the equations:

p + q = 834

and

2p + 3.5q = total profit

We need to determine whether 2p + 3.5q > 2000.

Statement One Only:

During the month, more units of P than units of Q were sold.

From statement one, we see that at least 834/2 + 1 = 418 units of P were sold, and at most 834/2 - 1 = 416 units of Q were sold. If exactly 418 units of P and 416 units of Q were sold, then the total profit is 2(418) + 3.5(416) = $2292, which is more than $2000. However, if 834 units of P and no units of Q were sold, then the total profit is 2(834) = $1668, which is less than $2000.

Statement one alone is not sufficient to answer the question.

Statement Two Only:

During the month, at least 100 units of Q were sold.

From statement two, we see that at least 100 units of Q were sold and at most 834 - 100 = 734 units of P were sold. If exactly 734 units of P and 100 units of Q were sold, then the total profit is 2(734) + 3.5(100) = $1818, which is less than $2000. However, if 418 units of P and 416 units of Q were sold, then the total profit is $2292 (see the analysis for Statement One Only), which is more than $2000.

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

With the two statements, it’s possible for the total profit to be more than $2000 (for example, 418 units of P and 416 units of Q were sold, for a total profit is $2292) or less than $2000 (for example, 734 units of P and 100 units of Q were sold, for a total profit is $1818).

The two statements together are still not sufficient to answer the question.

Answer: E

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