An antiques dealer purchased three cabinets at three distinc : GMAT Data Sufficiency (DS)
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# An antiques dealer purchased three cabinets at three distinc

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An antiques dealer purchased three cabinets at three distinc [#permalink]

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03 Jan 2013, 04:22
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An antiques dealer purchased three cabinets at three distinct costs last year and resold all three of those cabinets for three distinct prices this year. If the median price was received for the cabinet that had cost the median amount, and the antiques dealer made a 10% profit on that cabinet, did the dealer make more than a 10% profit margin on any one of the three cabinet sales?

(1) One of the cabinets sold for a price less than its original cost.
(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to purchase.
[Reveal] Spoiler: OA

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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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03 Jan 2013, 08:08
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From the question we get:

Median Price - Median Cost = 10 % Margin

(1) Is not sufficient, since it doesn't tell is whether the cabinet with the highest or lowest price was sold for a price less than the original cost
(2) We get the information that, the cabinet sold for the lowest price had the highest cost.
Hence the one with the highest Price must have had the lowest cost, so that together with the original statement we can conclude that:

Highest Price - Lowest Cost > 10% Margin , because the cabinet with the median price and median cost already had a 10% margin.

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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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04 Jan 2013, 03:14
daviesj wrote:
An antiques dealer purchased three cabinets at three distinct costs last year and resold all three of those cabinets for three distinct prices this year. If the median price was received for the cabinet that had cost the median amount, and the antiques dealer made a 10% profit on that cabinet, did the dealer make more than a 10% profit margin on any one of the three cabinet sales?

(1) One of the cabinets sold for a price less than its original cost.
(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to
purchase.

Hi,

Let C1,C2 and C3 be the Cost Price (CP increasing in that order) and S1,S2 and S3 are the Selling Price (SP increasing in that order)

Now given, (S2-C2)/C2*100= 10 % Profit Margin

From St1, We can have 2 cases i.e S1<C1 or S3<C3. But we don't know which one and we can only conclude on at least on one of these sale there will be a loss

From St 2, we get S1 was the Selling price of One Antique (Let it be Antique no 1) and C3 was the Cost Price

Now Imagine a case where the Selling price is same in all cases i.e S1=S2=S3=S

therefore, we have

C1<C2<C3 and

S1</ S2</ S3---->S1-C3<S2-C2< S3-C1---> S-C3<S-C2<S-C1---->Divide Eqn by C1 we get
(S-C3)/C1<(S-C2)/C1<(S-C1)/C1-----> (S-C3)/C1 <(S-C2)/C1<(S/C1-1)

Now (S-C2)/C2*100=10% this implies (S-C2)/C1*100> (S-C2)/C2*100 (Because C2>C1)

and therefore (S/C1-1) is greater than 10% and Hence Ans B

It looked tedious but wanted to arrive at the solution. I have taken the Selling price same for all is to get at minimum values of S and if at that minimum value if we can get a profit margin more than 10% then it will be also applicable for S1<S2<S3

Thanks
Mridul
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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25 Feb 2014, 05:58
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daviesj wrote:
An antiques dealer purchased three cabinets at three distinct costs last year and resold all three of those cabinets for three distinct prices this year. If the median price was received for the cabinet that had cost the median amount, and the antiques dealer made a 10% profit on that cabinet, did the dealer make more than a 10% profit margin on any one of the three cabinet sales?

(1) One of the cabinets sold for a price less than its original cost.
(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to purchase.

This was a bit hard to get at first but let's see. We are told that we have three cabinets and that the median price - median cost equals a 10% profit. Let's assume that median price is 11 and median cost is 10.

Statement 1 tells us that one of the cabinets sold for a price less than its cost. Let's assume that the highest price that paid by this cabinet was 18 and the cost 20 so of course he made a loss. But still the price of the remaining cabinet is less than 11 while the cost less than 10 and it is still possible to get a margin higher than 10% or lower (Eg. If price is 10 and cost is 1).

Insufficient

Statement 2 tells us that the cabinet with the highest cost also had the lowest price. Therefore if it had a cost higher than 10 and a price lower than 11 then obviously he lost some money again. But this means that the highest price is greater than 11 while the lowest cost is lower than 10, so we know that our profit margin >10%. Therefore this statement is sufficient

Sufficient

B

Hope this is clear
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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15 Apr 2014, 08:14
I am not able to understand why stmt 1 is not sufficient:
"If the median price was received for the cabinet that had cost the median amount"
It is given that received price is median of other two sales price: a fixed amount i.e. 10% ++ of median cost of that cabinet.

For statement one:
Cost price = 49 50 51
Sales price = X 55 Z (55=10% of 50)
Case 1: X = 49-1 = 48 then Y=62 (above 10% of 51+51) (48+62)/2 = 55
Case 2: X = 49-48=1 then Y=109 (above 10% of 51+51) (1+109)/2 = 55
Case 3: Z = 50 then X=60 (above 10% of 49+49) (50+60)/2 = 55
Case 4: Z= 1 then X=109 ( above 10% of 49+49) (1+109)/2 = 55

In all above cases to balance the prices with the median we will have to make adjustment in the sell price and that adjusted price is coming above 10% for particular cabinet.. as mentioned above...

Either I was not able to pick good numbers or A is also sufficient..

Kindly help to verify my solution.
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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15 Apr 2014, 10:17
PiyushK wrote:
I am not able to understand why stmt 1 is not sufficient:
"If the median price was received for the cabinet that had cost the median amount"
It is given that received price is median of other two sales price: a fixed amount i.e. 10% ++ of median cost of that cabinet.

For statement one:
Cost price = 49 50 51
Sales price = X 55 Z (55=10% of 50)
Case 1: X = 49-1 = 48 then Y=62 (above 10% of 51+51) (48+62)/2 = 55
Case 2: X = 49-48=1 then Y=109 (above 10% of 51+51) (1+109)/2 = 55
Case 3: Z = 50 then X=60 (above 10% of 49+49) (50+60)/2 = 55
Case 4: Z= 1 then X=109 ( above 10% of 49+49) (1+109)/2 = 55

In all above cases to balance the prices with the median we will have to make adjustment in the sell price and that adjusted price is coming above 10% for particular cabinet.. as mentioned above...

Either I was not able to pick good numbers or A is also sufficient..

Kindly help to verify my solution.

I too am with you on this one...
If a median number is increased by x% the corresponding numbers have to increase by X% to maintain the new number as a median..
So the third price has to increase by more than 10% to compensate for - 10% median increase + decreased rate at which the second case was sold..
So A satisfies too...
Btw rejected it at the first look..
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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15 Apr 2014, 10:18
JusTLucK04 wrote:
I too am with you on this one...
If a median number is increased by x% the corresponding numbers have to increase by X% to maintain the new number as a median..
So the third price has to increase by more than 10% to compensate for - 10% median increase + decreased rate at which the second case was sold..
So A satisfies too...
Btw rejected it at the first look..

Let us PM some expert to help on this
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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15 Apr 2014, 11:49
I think I am assuming Mean = Median..
So the error..
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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16 Apr 2014, 03:57
PiyushK wrote:
An antiques dealer purchased three cabinets at three distinct costs last year and resold all three of those cabinets for three distinct prices this year. If the median price was received for the cabinet that had cost the median amount, and the antiques dealer made a 10% profit on that cabinet, did the dealer make more than a 10% profit margin on any one of the three cabinet sales?

(1) One of the cabinets sold for a price less than its original cost.
(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to purchase.

I am not able to understand why stmt 1 is not sufficient:
"If the median price was received for the cabinet that had cost the median amount"
It is given that received price is median of other two sales price: a fixed amount i.e. 10% ++ of median cost of that cabinet.

For statement one:
Cost price = 49 50 51
Sales price = X 55 Z (55=10% of 50)
Case 1: X = 49-1 = 48 then Y=62 (above 10% of 51+51) (48+62)/2 = 55
Case 2: X = 49-48=1 then Y=109 (above 10% of 51+51) (1+109)/2 = 55
Case 3: Z = 50 then X=60 (above 10% of 49+49) (50+60)/2 = 55
Case 4: Z= 1 then X=109 ( above 10% of 49+49) (1+109)/2 = 55

In all above cases to balance the prices with the median we will have to make adjustment in the sell price and that adjusted price is coming above 10% for particular cabinet.. as mentioned above...

Either I was not able to pick good numbers or A is also sufficient..

Kindly help to verify my solution.

No, the first statement is not sufficient. Consider the cases below:
Attachment:

Untitled.png [ 9.49 KiB | Viewed 1510 times ]

Hope it helps.
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Re: An antiques dealer purchased three cabinets at three distinc [#permalink]

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16 Apr 2014, 04:13
Bunuel wrote:
PiyushK wrote:
An antiques dealer purchased three cabinets at three distinct costs last year and resold all three of those cabinets for three distinct prices this year. If the median price was received for the cabinet that had cost the median amount, and the antiques dealer made a 10% profit on that cabinet, did the dealer make more than a 10% profit margin on any one of the three cabinet sales?

(1) One of the cabinets sold for a price less than its original cost.
(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to purchase.

I am not able to understand why stmt 1 is not sufficient:
"If the median price was received for the cabinet that had cost the median amount"
It is given that received price is median of other two sales price: a fixed amount i.e. 10% ++ of median cost of that cabinet.

For statement one:
Cost price = 49 50 51
Sales price = X 55 Z (55=10% of 50)
Case 1: X = 49-1 = 48 then Y=62 (above 10% of 51+51) (48+62)/2 = 55
Case 2: X = 49-48=1 then Y=109 (above 10% of 51+51) (1+109)/2 = 55
Case 3: Z = 50 then X=60 (above 10% of 49+49) (50+60)/2 = 55
Case 4: Z= 1 then X=109 ( above 10% of 49+49) (1+109)/2 = 55

In all above cases to balance the prices with the median we will have to make adjustment in the sell price and that adjusted price is coming above 10% for particular cabinet.. as mentioned above...

Either I was not able to pick good numbers or A is also sufficient..

Kindly help to verify my solution.

No, the first statement is not sufficient. Consider the cases below:
Attachment:
Untitled.png

Hope it helps.

Thanks Bunuel, now I am able to identify the error: I was considering median=mean, a silly mistake.
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