Hi!
As always, let's start by identifying the exact question: what's the gross profit?
Well, gross profit = total revenue - total cost. We're given the total cost of $600, so we need to find the total revenue.
We're told that 2/3 of the heads were sold for 25% above cost/head. There are two ways to calculate the revenue for this batch.
First, we could figure out the price/head = total cost/total # = $600/1500 = $6/15 = $2/5 = $.4
An increase of 25% on 40 cents is an extra 10 cents, so the selling price of each head is $.5. Multiply that by the number sold (2/3 * 1500=1000) to get:
1000 * $.5 = $500
While that solution would make your grade 8 math teacher proud and get you a gold star, on the GMAT we're more concerned about speed than elegance. So, the quicker way to solve for revenue is to avoid converting to individual units.
Since we sold 2/3 of the batch, the cost for those heads is 2/3 the total cost.
2/3($600) = $400
We know we marked the batch up by 25%, so the selling price for this batch is:
1.25($400) = $500... done!
Next up is the day 2 batch, which were sold for 10% less than the day 1 batch.
If we calculated the individual sale price at 50 cents on day 1, we take 90% of that to get 45 cents on day 2. There were 500 heads left, so:
$.45 * 500 = $225
If we calculated the full batch revenue for day 1, we have to approach day 2 differently. There are a couple of approaches we could take.
1) compare the quantities. Since we sold 2/3 on day 1 and 1/3 on day 2, we sold half as many on day 2 as day 1 (1/3 is one half of 2/3). So, at day 1 prices, the revenue for day 2 would have been half of $500 which is $250. We sold at a 10% discount, so the actual selling price for day 2 is:
.9($250) = $225
2) do the actual math. First we marked up by 25%, then down by 10%, so we get:
cost * 1.25 * .9 = cost * 5/4 * 9/10
The cost of the day 2 batch is 1/3 the total cost, so $200. Therefore, our day 2 revenue is:
$200*5/4*9/10 = $9000/40 = $900/4 = $225
Adding our revenue together:
total revenue = $500 + $225 = $725
And, finally, subtracting total cost, we get:
gross profit = $725 - $600 = $125... choose C!
grandh01 wrote:A shipment of 1,500 heads of cabbage,
each of which was approximately the
same size, was purchased for $600.
The day the shipment arrived,
2/3 of the heads were sold, each at 25
percent above the cost per head. The
following day the rest were sold at a
price per head equal to 10 percent less
than the price each head sold for on
the day before. What was the gross
profit on this shipment?
(A) $100
(B) $115
(C) $125
(D) $130
(E) $135
