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In the month of November, a company sold 3000 items of model A and 1000 items of model B. Items of model A accounted for 60% of the company's monthly sales in dollars while items of model B accounted for 40% of the monthly sales in dollars. If the company had sold 1000 items of model A less than it actually did, what percent of the total monthly sales in dollars would have been attributed to model A?

In the month of November, a company sold 3000 items of model A and 1000 items of model B. Items of model A accounted for 60% of the company's monthly sales in dollars while items of model B accounted for 40% of the monthly sales in dollars. If the company had sold 1000 items of model A less than it actually did, what percent of the total monthly sales in dollars would have been attributed to model A?

A. 48 B. 50 C. 52 D. 54 E. 55

Let \(S\) denote the total November sales of the company. The price of an item of model A = \(0.6*\frac{S}{3000}\); the price of an item of model B = \(0.4*\frac{S}{1000}\). If the company had sold 2000 items of model A, the revenue from sales of model A would have amounted to \(0.6*\frac{S}{3000}*2000 = 0.6S*\frac{2}{3} = 0.4S\) which is equal to the revenue from sales of model B. So, in the hypothetical case described in the stem, the two models would have accounted for 50% of the monthly sales each.

Alternative explanation - picking numbers

Let the total revenue be \($10,000\); then revenue from Model A is \($6,000\) for 3,000 units or \($2\) per unit and Model B's revenue is \($4,000\) for 1,000 units or \($4\) per unit.

If we had sold only 2,000 units of model A, the total revenue would have been \($2*2,000 +$4*1,000 =$8,000\). At this point it is clear that model A and B bring equal amounts of revenue (\($4,000\) each) and half of monthly sales are attributed to model A.

In the month of November, a company sold 3000 items of model A and 1000 items of model B. Items of model A accounted for 60% of the company's monthly sales while items of model B accounted for 40% of the monthly sales. If the company had sold 1000 items of model A less than it actually did, what percent of the total monthly sales would have been attributed to model A?

A. 48 B. 50 C. 52 D. 54 E. 55

Here's one more approach: 60%=20%+20%+20%, 40%=20%+20% --> 3000/3=1000=20%, 1000/2=500=20% ==> 1000a=500b means b=2a 2000a/2000a+2000a (=1000b) = 50%
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the question never specifies that monthly sales are in dollars...where as monthly sales can be numbers also... what if 60% of A is 3000 units.. so monthly sales is 5000 units..

I agree with vijayjec02, the question stem was a bit confusing. I had to assume that may be question intends to mean this. Question asked "A company sold 3000 items of model A and 1000 items of model B" and then says "Items of model A accounted for 60% of the company's monthly sales."

Item of model A did not amount for 60% of sales... items amount for 75% of total sales. Money generated from the sale of item A amounted for 60%...

The question stem is not clear in this case because monthly sales can be in terms of both money and quantity. Bunuel, I request you to replace this question stem to avoid any ambiguity in the meaning of the stem.

The question stem is not clear in this case because monthly sales can be in terms of both money and quantity. Bunuel, I request you to replace this question stem to avoid any ambiguity in the meaning of the stem.

I too agree. The question stem never specifies the sales in terms of revenue or number of items.

The question stem is not clear in this case because monthly sales can be in terms of both money and quantity. Bunuel, I request you to replace this question stem to avoid any ambiguity in the meaning of the stem.

I too agree. The question stem never specifies the sales in terms of revenue or number of items.

Thank you. Edited as suggested. Hope now it's clear.
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