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easy ds question with weird wording

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by missrochelle » Thu Aug 26, 2010 6:32 pm
23. og12

The profit from the sale of an appliance increases, though not proportionally, with the number of units sold. Did the profit exceed $4mm on the sales of 380,000 units?

1) The profit exceeded $2mm on sales of 200,000 units.
2) The profit exceeded $5mm on sales of 350,000 units.


OA. B


When i looked at the problem, i tried ot solve stmt 1 as an inequality. 200,000(profit per unit) > 2,000,000.

therefore (profit per unit) > 10. Substituting 11 as the minimum I get 380,000 units * 11 = $4,180,000 as the minimum. So I thought stmt was also sufficient.

Is the takeaway here that "THOUGH NOT PROPORTIONALLY" means you cant divide out per unit price because the price varies?
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by 4GMAT_Mumbai » Thu Aug 26, 2010 7:08 pm
missrochelle wrote: therefore (profit per unit) > 10. Substituting 11 as the minimum I get 380,000 units * 11 = $4,180,000 as the minimum. So I thought stmt was also sufficient.
Several not-so-right assumptions. If it is not 10, why cannot it be 10.2 ? Even if it is 11, it would not be 11 on all the 0.38m units ...
missrochelle wrote:Is the takeaway here that "THOUGH NOT PROPORTIONALLY" means you cant divide out per unit price because the price varies?
The takeaway here is that when the # of units increases, profit DOES increase but not in an uniform manner.

A geometric interpretation: You will not be able to plot a straight line with 'units' on the x-axis and 'profit' on the y-axis. It would be a jagged line with varying slopes.

Which is why 2 is sufficient. If the profit with 350,000 units exceeds $5m, the profit from the sale of 380,000 units will definitely exceed $4m (in fact, it will definitely be higher than $5m itself - It could be very little - $5,000,010 or very high - $10m, say).

Hope this helps. Thanks.
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4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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by Rahul@gurome » Thu Aug 26, 2010 7:25 pm
Here, by doing the above calculations you are assuming that the profit is increasing proportionally with the number of units sold when actually the main statement is just saying that there is an increase in profit with the number of units sold.
Consider just statement (1).
It says that profit exceeds $2mm on sales of 200,000 units.
It may be that profit is $2.000001mm on sales of 200,000 units, $2.0000015mm on sales of 200,001 units, $2.0000016mm on sales of 200,002 units and so on.
In such a case profit may not exceed $4mm on the sales of 380,000 units.
So statement (1) alone is not sufficient.

Next consider statement (2) alone.
It is already exceeding $5mm on sales of 350, 000 units .
So obviously, since profits are not going to decrease, for sale of 380, 000 units profit will exceed $4mm.
So (2) alone is sufficient.
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