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the most expensive product

by sanju09 » Mon Apr 12, 2010 3:40 am
Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) $2,600
(B) $3,900
(C) $7,800
(D) $11,800
(E) $18,200
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by srinivasarajui » Mon Apr 12, 2010 3:47 am
IMO D.

Will post the explanation a while latter.
Srinu
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by blaster » Mon Apr 12, 2010 4:25 am
(420 * 10 + 14*1000 + x) / 25 =1200

x = 11800

best aproximation is D
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by liferocks » Mon Apr 12, 2010 4:40 am
I am also getting D but approach is slightly different

average 1200
10 product for $420 so difference from average is (10*780)=$7800 -->this shows that it can only be option D or E
14 prod for $1000 so difference from average is (14*200)=$2800

so price (1200+2800+7800)..digit in 100th place is 8 hence option D

this does not really requires calculation so process becomes faster.
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by harshavardhanc » Mon Apr 12, 2010 5:20 am
sanju09 wrote:Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) $2,600
(B) $3,900
(C) $7,800
(D) $11,800
(E) $18,200
approach : minimize the cost of all the products, except one, while maintaining the average.

at the most 10 products can be $420 = i.e 780 less than the avg. ---> we get $7800
next, at the most 14 products can be $1000 --> giving us 14 * $200 = $2800

this amount (7800 + 2800) can be added to the remaining $1200, which makes it $11,800. Hence, D.
Regards,
Harsha
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