knight247 wrote:In a department store, the average daily stock of an item for a 7-day period is the average (arithmetic mean) of the closing stock of the item on each of the 7 days. The closing stock of a certain item at the start of one 7-day period was 600 units. During the period, 300 units of the item were sold on one particular day. No other receipt or sale of the item occurred during the period. What was the average daily stock of the item for the 7-day period?
(1)The sale of 300 units of the item took place on the 4th day of the 7-day period.
(2)The average daily stock of the item till the 5th day of the 7-day period was 480 units.
OA is D
Hello!
The solution to this one is actually quite boring considering how convoluted the wording is. Basically we need to add up the closing stock for each day and divide it by 7 to get the average closing stock. And since only one sale took place and we know the amount of this sale, we need only know when this sale took place.
Statement (1) allows you to do this. This tells us that closing stock was 600 at the ends of days 1, 2 and 3 and that it was 300 at the ends of days 4, 5, 6 and 7. So we take:
(600 * 3 + 300 * 4)/7
Statement (2) is a little bit less obvious. However, there are two aspects to the statement that give us the information we need to conclude with the solution:
- - If the average of the stocks on the first five days (and on the GMAT I think they should say "up to and including the 5th day" just to make it abundantly clear that was what they meant--where did you pull this problem from?) was 480, it follows that the sum of the stocks on the first five days was 480 * 5.
- If the average of the stocks on the first five days was less than the original amount, it follows that the sale took place before the fifth day. Therefore, we know that the closing stock on each of the last two days was 300.
Therefore, we can calculate the average as follows:
(480 * 5 + 300 * 2)/7
So, yes,
D is correct!
