Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000


The table above shows the total sales recorded in July for the 5 salespeople. It was discovered that one of Cal’s sales was incorrectly recorded as one of Ann’s sales. After this error was corrected, Ann’s total sales were still higher than Cal’s total sales, and the median of 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?

The answer is $120,000. GMAT-Prep Exam 2

Hi Instructors,
I know that the median is the less than half of the numbers and greater than half of the numbers if I understand correctly. Here, we have an odd set of numbers and the median as stated above is 330,000 in dollars. To get the answer, is it correct to subtract 330,000 from 450,000 to get the answer, that is, 120,000, since 450,000 is the correct value. Did I answer this correctly? If not, why or if so, why? What is the rationale behind this type of problem?

Your response is greatly appreciated....

Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000


The table above shows the total sales recorded in July for the 5 salespeople. It was discovered that one of Cal’s sales was incorrectly recorded as one of Ann’s sales. After this error was corrected, Ann’s total sales were still higher than Cal’s total sales, and the median of 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?

Since the Median of the 5 sales with the 3rd highest sale when arranged in ascending order, we know that $330,000 is one the sale numbers.

Setting these numbers in ascending order:

Cal $190,000
Dot $210,000
Bob $360,000
Ann $450,000
Ed $680,000

Thus, before the correction the median is 360,000 and after the correction the median is 330,000.
Thus from that either Ann's new sale is 330,000 or Cals adjusted sale is 330,000.

Case I:
Anns new sale: 330,000
Cals new sale: 190000 + (450000-330000) = 310000
And the second statement still holds true : Ann's new sale > Cals new sale

Case II
Cals new sale : 330,000
Anns new sale 450000 - ( 330000 - 190000) = 310000
However in this case the second statement does not hold true: Anns new sale < Cals new sale

There fore case I has to be true

The value of incorrectly recorded sale : 450000-330000 = 120000

Hi instructors,

Thanks for the explanation you have provided. I have one doubt. Could you please expand on what you mean when you subtract $330,000 from $450,000 to get $120,000. You have provided two scenarios, however, I am not to clear but what you mean when you say Ann's sales income is now $330,000 when it states that it has not decreased. Are you not trying to find out the missing amount? Did I miss something?

Moreover, I know the median is greater than half of the numbers in the set and less than half of the numbers in the set. Here, we have an odd set of numbers and with a median of $330,,000 when Ann's and Cal's sales income is correctly adjusted. My question is it correct to subtract $330,000 from $450,000, and if so why? A brief explanation would be greatly appreciated for future reference.

Thank you

ok, so here are some basic facts in this problem. each of them can lead to a takeaway about these types of problems.

fact one:
there are an odd number of data points, so the median is actually one of the numbers in the problem.
this is cool here, because you know that exactly one of two things has happened: (a) cal's new total is $330,000, (b) ann's new total is $330,000. since none of the other salespeople's totals are going to change, it's impossible for the new median to be anyone's other than ann's or cal's.

fact two:
however much you take away from ann's sales, you have to add to cal's sales.
you're basically just exchanging money between the two of them, so whatever dollars you take away from ann must go to cal.

fact three:
in any problem like this one, you should put the salary figures in order.
this goes without saying in any problem that has to do with the median of a set. divya's post above does a nice job of this.

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as for your question of whether we can subtract 330,000 from 450,000, the GENERAL answer is: no, you can't.
you see, there are two possible cases, as remarked above: (a) cal's new total is $330,000, (b) ann's new total is $330,000.
if (a) turns out to be the correct case, then the value of the sale will be $330,000 - $190,000 (i.e., the change in cal's money), NOT $450,000 - $330,000 (because, if that's the case, then it turns out that the $330,000 figure has nothing at all to do with ann).
if (b) turns out to be the correct case, then the value of the sale will be $450,000 - $330,000 (i.e., the change in ann's money), and cal's $190,000 will have nothing to do with the $330,000 figure.

in this problem, it just so happens that ann's new total is the $330,000, so $450,000 - $330,000 is the value of the sale. however, if different conditions were given, it could just as well have been the case that $330,000 is cal's new total (not ann's), and then that subtraction wouldn't work.

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by the way, divya is not one of our instructors (although her posts are of consistently high quality - thanks divya).