An antiques dealer purchased three cabinets at three distinc

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.

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..

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:

Hope it helps.

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.

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