An antiques dealer purchased three cabinets at three distinc

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
Cheers
J

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..

Let us PM some expert to help on this

I think I am assuming Mean = Median..
So the error..

No, the first statement is not sufficient. Consider the cases below:
Hope it helps.

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

Bunuel Can you please confirm how the answer is B?

I am getting E as an answer. Below is my explanation

Case1: no profit is greater than 10%
Cabinet#: 1 2 3
Cost: 10 20 30
Selling Price: 11 22 9

Case2: Profit is greater than 10%.
Cabinet#: 1 2 3
Cost: 10 20 30
Selling Price: 13 22 9

In Case 1 the selling price of 22 is not the median selling price anymore. So this is not a valid case!

MartyMurray KarishmaB Can you please provide an 'easy to understand' solution to this question ?

In case of calculating profit margin the denominator needs to contain 'S2' ..I think. Bunuel

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?

The passage tells us that the antiques dealer made a 10% profit on the cabinet that cost the median amount. So, we know that the dealer did not make more than a 10% profit on the median cost cabinet. Thus, to answer the question, we have to determine whether we can tell for sure whether the dealer made more than a 10% profit on either of the other two cabinets.

(1) One of the cabinets sold for a price less than its original cost.

We know from the passage that one cabinet was sold for a 10% profit and that that cabinet was sold for the median selling price.

Now, this statement tells us that one of the cabinets sold for a price less than its original cost.

We are still left not knowing whether the third cabinet was sold for a greater than 10% profit.

After all, the cabinet that was sold for less than its cost could have been the cabinet with the lowest cost. In that case, the highest priced cabinet could have been sold for a profit that was greater or less than 10%.

Alternatively, the cabinet that was sold for less than its cost could have been the highest priced cabinet, which could have cost much more than the median cost cabinet, in which case the highest cost cabinet could still have sold for a price greater than the median selling price. Also, the lowest priced cabinet could cost have much less than the median cost cabinet and thus had room to sell for more or less than a 10% profit and still have been sold for less than the median selling price.

So, essentially, this statement tells us that a second cabinet was sold for a profit less than 10% but leaves open the possibility that the third could have been sold for a profit greater or less than 10%.

Insufficient.

(2) The cabinet that sold for the lowest price was the one that cost the antiques dealer the most to purchase.

This statement tells us that the lowest selling price was that of the highest cost cabinet.

We already know that the median cost cabinet sold for the median price.

Thus, the lowest cost cabinet must have sold for more than the median price. After all, only in that way would the selling price of the median cost cabinet have been between the selling prices of the other two.

In that case, since the median cost cabinet was sold for a 10% profit, the lowest cost cabinet must have been sold for a profit greater than 10%. After all, the lowest cost cabinet's cost was lower than that of the median cost cabinet, and its selling price was higher than that of the median cost cabinet.

Sufficient.

Correct answer: B