Data Sufficiency

The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. Did the profit exceed $4 million on sales of 380,000 units ?
(1) The profit exceeded $2 million on sales of 200,000 units.
(2) The profit exceeded $5 million on sales of 350,000 units.





Answer is B ... can someone please explain how this is true?

We know the profit goes up as the number of units goes up. However, it does not go up proportionally. We want to know if the profit exceeded $4 million from sales of 380,000 units.

(1) Knowing the profit exceeded $2 million on the sales of 200,000 units tells us nothing because the profit does not increase proportionally. The next 180,000 units could have profits that exceed an additional $2 million, but they could also be associated with profits that only exceed an additional $1 million. Since we don't know how the profit goes up with each unit, we cannot answer this. INSUFFICIENT

(2) Knowing the profit exceeded $5 million on the sales of 350,000 units DOES tell us something. We have already exceeded our profit of $4 million in sales with 30,000 units to spare. We also know that the profits increase as sales increase. So even if the profits are less than $0.01 per appliance, our profits from sales of 380,000 units will be greater than $4 million. SUFFICIENT

B

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

(1) The profit exceeded $2 million on sales of 200,000 units.

Profit on sales of 380,000 units is > Profit on sales of 200,000 units ($2 million). Profit on sales of 380,000 units can be $10million or $3million. Hence Insufficient!

(2) The profit exceeded $5 million on sales of 350,000 units.

Profit on sales of 380,000 units is > Profit on sales of 200,000 units($5 million).Hence Sufficient!

Option B

But the question says that " though not proportionally " so we can't assume profit would be directly proportional number of units sold. However, Answer can be B, if we assume that there is no loss at all so that last (380,000 - 350,000) = 30,000 items will contribute very less profit.

Please reply if i am thinking wrong?

ahhh i see now!! why do i keep making these silly mistakes!? hopefully i can get these mistakes out now so test day i'll beat the gmat!

i'm going to take a shot at responding to amit's question ... please correct me if my reasoning is flawed.

-- statement 2 states that our target profit of $4mm has already been met on sales of 350m units. i think i see what you are saying here ... "well what happens if they gave away the remaining 30m units and actually took a loss large enough on those to make us not reach our target profit of $4mm?"

well the answer to this question is in the question stem itself "the profit from the sale of a certain appliance increases, .... with the number of units sold." translation ... they didnt sell/dump the remaining 30m appliances at below cost because a profit is always made. he could sell the remaining 30m units for a profit of $.01 per unit and the statement will still yield the same answer ... thus a is the correct answer.