The table above shows the total sales recorded in July for

There are 5 values given to us and their median is 330 (Let's ignore the extra 0s). What does that mean?

Say there is a list of numbers: 4, 6, 9, 12, 35
How do you get the median? It is the middle value in case you have odd number of values in increasing/decreasing order. It doesn't matter what the other values are. Median is equal to the value right in the middle.

If median of a list of 5 values is 330, it means that 330 must be one of the 5 values. 2 values must be greater than 330 and 2 must be smaller than 330.

Let me arrange the given list in decreasing order:

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

680, 450, 360, 210, 190
I cannot touch the other 3 values (Just the red ones (Ann's and Cal's)). Since 680 and 360 remain and are greater than 330, so my actual list should look something like this:

680, 360, 330, ....., ..... (210 occupies one of these blanks)

The question now is: To whom does this 330 belong?

If Ann's sales decreases from 450 to 330, Cal's sale should increase by 120 (= 450 - 330) i.e. Cal's actual sales should be 190 + 120 = 310.
The list becomes: 680, 360, 330, 310, 210 - satisfies everything. The value of the incorrectly recorded sales must have been $120,000.

Could 330 belong to Cal? Then Cal's sales would have increased by 330 - 190 = 140
Ann's sales would have decreased by 140 to get her actual sales of 310. But it is given that Ann's sales remains higher than Cal's. Hence this is not possible.
_________________

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 at Acme Truck Sales. 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 the 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?
A. $30,000
B. $48,000
C. $90,000
D. $120,000
E. $140,000

Old sales: {Cal=190, 210, 360, Ann=450, 680}.

Now, the median of a set with odd # of terms is just the middle term (when ordered in ascending /descending order). So, old median=360.

We know that new median=330 and Cal's sales are still less than Ann's, hence Ann's new sales must be 330 (Ann's sales # must be reduced so that it becomes the middle term: 360 and Ann must switch places): {210, Cal, Ann=330, 360, 680}.

The value of the incorrectly recorded sale is Ann's old sales - Ann's new sales = 450 - 330 = 120.

Answer: D.

Hope it's clear.
_________________

CAL 190,000+X
DOT 210,000
ANN 450000-X
BOB 360,000
ED 680,000

Median is middle value if the number of terms are odd.

Hence, 450000-x = 330,000
x=120,000

OA. D
_________________

A 4,50,000
B 3,60,000
C 1,90,000
D 2,10,000
E 6,80,000

Problem lies with sales of A & C...i.e. A' sales value 4,50,000 will have to be reduced by x and C's sales value will have to be increased by x. ( given in the problem )

After the correction/rearrangement the median value is 33,000

Keeping the other 3 sales values of B,D,E intact

?,2,10,000,3,30,000 (median),3,60,000,6,80,000

Two possibilities are there :

1.C's sales value of 1,90,000 would have been increased to 3,30,000..In that case, A's sales value becomes 3,10,000.
This goes against the given information that A's sales is still higher than C.

2.So, we can conclude that A's sales value has been decreased to 3,30,000.
Hence the incorrect value = 4,50,000 - 3,30,000 = 1,20,000

Hope I've made sense..Probably I've made it lengthy...!!!

Hi Bunnel

Here how do we now that Ann's sales=330. The question says ann's sales were higher than cal's and we are not sure about any particular value and we too don't know how much cal's sales were increased, so how can we order the list in the this way

{210, Cal, Ann=330, 360, 680}.

Plz correct me if i am wrong

First of all either Cal's or Ann's sales must be 330. Now, if Cal's sales are 330 then as Ann>Cal then the ordering would be {210, Cal=330, Ann>Cal, 360, 680} --> median={Ann's sales}>330, but we know that the median is 330, so this case is not possible.

Hope it's clear.
_________________

ya that makes sense...

I always miss reading small parts in a sentence...

Let the transaction amount be x. Given that 450,000-x>190,000+x --> 2x<260,000 --> x<130,000

Now the new median is 330,000. As the only 2 values changing are that of Cal's and Ann's, this new median must be either the increased sales figure of Cal, or the deflated sales figure of Ann.

Cal : 330,000-190,000 =x = 140,000--> Not possible as x<130,000. Thus the median is the new sales figure of Ann --> 450,000-330,000 = 120,000.
D.
_________________

HI All,

Karishma's explanation is spot-on, so I won't rehash any of that here. I do want to point out that if the original poster had included the 5 answer choices, then we could have used them against the prompt and TESTed THE ANSWERS. That approach likely would have been easier (and taken less time) than the approach that we are all forced to take without having the answer choices. Remember that most questions on the Official GMAT can be approached in more than one way. Having the flexibility to solve problems in multiple ways can help you to score at a higher level on Test Day.

GMAT assassins aren't born, they're made,
Rich

Median has to be the 3rd value. There is no 330k right now. So either Ann's or Cal's sale has to become 330k.

If Ann's sale becomes 330k, it means her sale decreases by 120k so Cal's increases by 120k and becomes 310k.
If Cal's sale becomes 330k, it means her sale increased by 140k so Ann's must decrease by 140k to become 310k. But we are given that Ann's sale is still more than Cal's sale even after correction. So Ann's 310 and Cal's 330 is not possible.
It must be Ann's 330 and Cal's 310 then.
_________________

33 is median so now re arrange the given value in ascending order keeping 33 in middle

(45-33),21,33,45,68

carl sales ; 12+19 ; 31

IMO D 120,000

SInce,
Median is not given in the table and is mentioned as 330k, then either Cal or Anne's new salary would have to be 330k.

Condition even after correction salary of Sal< Ann

(190 +x) < (450 -x)

check by plugging in options, lets start with option E 140 in this case. 190 + 140 = 330
and 450-140 = 310 which violates the given condition,
only option satisfying the condition is option D 120K

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________