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The table above shows the total sales recorded in July for the 5 sales [#permalink]

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05 Dec 2008, 20:31

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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

Re: The table above shows the total sales recorded in July for the 5 sales [#permalink]

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24 Jul 2011, 21:25

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Expert's post

snowbirdskier wrote:

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

The table above shows the total sales recoreded 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? (GMAT practice test)

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. _________________

The table above shows the total sales recorded in July for [#permalink]

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01 Feb 2012, 08:01

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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 _________________

Re: The table above shows the total sales recorded in July for [#permalink]

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01 Feb 2012, 10:43

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Expert's post

1

This post was BOOKMARKED

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.

Re: The table above shows the total sales recorded in July for [#permalink]

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01 Feb 2012, 16:20

Bunuel wrote:

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 a 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.

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

Re: The table above shows the total sales recorded in July for [#permalink]

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01 Feb 2012, 16:25

Expert's post

kotela wrote:

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.

Re: The table above shows the total sales recorded in July for [#permalink]

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01 Feb 2012, 18:22

Bunuel wrote:

kotela wrote:

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... _________________

Re: The table above shows the total sales recorded in July for [#permalink]

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23 May 2013, 10:59

Expert's post

mydreammba wrote:

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

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. _________________

Re: The table above shows the total sales recorded in July for [#permalink]

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26 May 2013, 00:53

mydreammba wrote:

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

Can anyone please help with this......

My approach: As question stem tells that median is 330000, take a quick look for the other salesmen to match this median. None has 330000 sales. Thus this must of of either Ann's or cal's.

besides that question further tells ann's and cal's amount is misplaced. so let us try to make Ann's sells 330000. Then we have to reduce 12000. this will be added to cal's and become 310000. this satisfies the condition that:

Ann's sales amount > Cal's sales amount.

To verify check by making Cal's amount 330000 above mentioned condition will be violated.

Thus The misplaced amount is 120000. _________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

Re: The table above shows the total sales recorded in July for [#permalink]

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24 Jul 2014, 05:36

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Re: The table above shows the total sales recorded in July for the 5 sales [#permalink]

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Re: The table above shows the total sales recorded in July for the 5 sales [#permalink]

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06 Mar 2015, 18:51

Expert's post

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.

Re: The table above shows the total sales recorded in July for [#permalink]

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14 May 2016, 08:35

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).

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