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# A company produces and sells two different products. Product A sells f

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Q51  V47
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Re: A company produces and sells two different products. Product A sells f [#permalink]
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thakurarun85 wrote:
The answer is D. Correct me if I am wrong.

There appears to be an error near the top of your solution, in the line beginning "1)...". You rewrite the equation 1,500,000 = 5a + 4b as k = 1,500,000 - 3b, but if you just replace k with 2a + b, which is how you've defined k, you'll see those two equations aren't the same; the second equation would need to say k = 1,500,000 - 3b - 3a, or you'd need different coefficients. You also didn't analyze Statement 2 alone, and that Statement is clearly insufficient (because the company could sell merely one product of each type, in which case they certainly lose money).

I explained this above using an algebraic approach, because I was replying to someone using an algebraic solution, but this problem is really just a weighted average question. The company earns revenue from two sources. Ignoring the \$500,000 fixed cost for now, on one source, they make a 25% profit (costs are 75% of revenue) and on the other they make a 40% profit (costs are 60% of revenue). So when we combine the two revenue streams, the profit will be somewhere between 25% and 40%. When we learn the company earns more revenue from the more profitable source, we learn that their percent profit is above the midpoint of 25% and 40%, so is above 32.5%. We know also their total revenue is \$1,500,000. So the company makes between 32.5% and 40% of \$1,500,000 in profit, before we consider their fixed cost. We want to know if that profit exceeds the \$500,000 fixed cost. And we can't tell, because 0.325*1,500,000 is just less than \$500,000, while 0.4*1,500,000 is greater than \$500,000. So the answer is E. You can prove that numerically if you want to; if you let the revenue from A be \$800,000 and let the revenue from B be \$700,000, and work out the total costs, you'll find they exceed the total revenue by a very small amount.
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Re: A company produces and sells two different products. Product A sells f [#permalink]
This Yes/No question provides the selling prices and cost structure for a company producing two products and asks whether revenues exceeded costs. Information that gives an unambiguous answer of yes or no will be sufficient, even if you cannot determine exactly what revenues or costs were.

Convert this word problem into algebra. Let a be the number of units of product A produced and sold and let b represent the number of units of product B produced and sold.

The equation for revenue is selling price times quantity. So, Revenue = \$5a + \$4b.

The variable cost for each unit of product A is 60% of \$5 or 0.60 × \$5, which is \$3, and the variable cost for each unit of product B is 75% of \$4 or 0.75 × \$4, which is also \$3. The company also has \$500,000 of fixed costs each year. Thus, Cost = \$3a + \$3b + \$500,000.

The question asks whether revenue exceeds costs, which translates to "Is 5a + 4b > 3a + 3b + 500,000?" This further simplifies to "Is 2a + b > 500,000?"

Evaluate the statements

Statement (1) says that total sales were \$1,500,000 but provides no breakdown of sales between the two products. So, 1,500,000 = 5a + 4b and Cost = 3a + 3b + 500,000. There are now two equations and three variables: Cost, a, and b. Thus, Statement (1) is insufficient; eliminate (A) and (D).

Statement (2) says that the revenue from product A exceeded the revenue from product B, or 5a > 4b. Lacking any information about a or b individually, you can't solve for a and b or for 2a + b. This statement is insufficient. Eliminate (B) and proceed to evaluate the statements together.

Since Statement (1) has two equations and three variables and Statement (2) is an inequality (not an equation), there's still no way to get a or b individually or (2a + b). Therefore, even taken together, the statements are insufficient. (E) is correct.

TAKEAWAY: Convert word problems into algebra before evaluating the statements so that you know what information is needed to determine sufficiency.
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Re: A company produces and sells two different products. Product A sells f [#permalink]
All in all without the number of A and B products sold, it will be impossible to tell the total variable cost of production- hence impossible to calculate ROI

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Re: A company produces and sells two different products. Product A sells f [#permalink]
thinkvision wrote:
This Yes/No question provides the selling prices and cost structure for a company producing two products and asks whether revenues exceeded costs. Information that gives an unambiguous answer of yes or no will be sufficient, even if you cannot determine exactly what revenues or costs were.

Convert this word problem into algebra. Let a be the number of units of product A produced and sold and let b represent the number of units of product B produced and sold.

The equation for revenue is selling price times quantity. So, Revenue = \$5a + \$4b.

The variable cost for each unit of product A is 60% of \$5 or 0.60 × \$5, which is \$3, and the variable cost for each unit of product B is 75% of \$4 or 0.75 × \$4, which is also \$3. The company also has \$500,000 of fixed costs each year. Thus, Cost = \$3a + \$3b + \$500,000.

The question asks whether revenue exceeds costs, which translates to "Is 5a + 4b > 3a + 3b + 500,000?" This further simplifies to "Is 2a + b > 500,000?"

Evaluate the statements

Statement (1) says that total sales were \$1,500,000 but provides no breakdown of sales between the two products. So, 1,500,000 = 5a + 4b and Cost = 3a + 3b + 500,000. There are now two equations and three variables: Cost, a, and b. Thus, Statement (1) is insufficient; eliminate (A) and (D).

Statement (2) says that the revenue from product A exceeded the revenue from product B, or 5a > 4b. Lacking any information about a or b individually, you can't solve for a and b or for 2a + b. This statement is insufficient. Eliminate (B) and proceed to evaluate the statements together.

Since Statement (1) has two equations and three variables and Statement (2) is an inequality (not an equation), there's still no way to get a or b individually or (2a + b). Therefore, even taken together, the statements are insufficient. (E) is correct.

TAKEAWAY: Convert word problems into algebra before evaluating the statements so that you know what information is needed to determine sufficiency.

the company sold the same number of units of each product as it produced. => a and b are equal ....
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Re: A company produces and sells two different products. Product A sells f [#permalink]
To come up 1.5M revenue within “ the company sold the same number of units of each product as it produced.” statement a=b It should produce 166666.7777 products each. This makes No profit or no loss and give Yes to A.

Which point did I miss?

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Re: A company produces and sells two different products. Product A sells f [#permalink]
The answer is D. Correct me if I am wrong.
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Re: A company produces and sells two different products. Product A sells f [#permalink]
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