Max price of an item

[Sonu]

Hi all,

I was working on some Quant problems from my Kaplan book and had a question about one question. I was wondering about the best and simplest way to solve this kind of a problem. Also, does this sound like a medium or difficult question ?

Q) At an auction, a line of 25 items were sold with an average price of $1200. If none of the items were sold for less than $420 and exactly 10 items were sold for less than $1000, what is the greatest possible selling price of the most expensive product ?

A) 2600
B) 3900
C) 7800
D) 11800
E) 18200

[Guest]

In this type of question, the approach I would use is calculating the extremes. Since there are 25 items and the avg selling price is $1200. We can find the total sum by multiplying it out. The total sum of the 25 items are $30000.

The question states that no item was sold for less than $420 and EXACTLY 10 items sold for less than 1000. So, to maximize the highest selling item, we can choose the price of $420 for all 10 of those items that sold for less than 1000. This would total $4200.

So, that leaves us with 15 items left to find values for. If the next 14 items sold for $1000 each (since it satisfies the constraint of each item being greater than $420 and the 10 items <1000 are accounted for) thus totalling $14000.

The highest price of the most expensive item, therefore will be $30000 - $14000 - $4200 = $11,800.

Hi all,

I was working on some Quant problems from my Kaplan book and had a question about one question. I was wondering about the best and simplest way to solve this kind of a problem. Also, does this sound like a medium or difficult question ?

Q) At an auction, a line of 25 items were sold with an average price of $1200. If none of the items were sold for less than $420 and exactly 10 items were sold for less than $1000, what is the greatest possible selling price of the most expensive product ?

A) 2600
B) 3900
C) 7800
D) 11800
E) 18200

[Sonu]

Thank you for the explanation....

[RonPurewal]

In this type of question, the approach I would use is calculating the extremes. Since there are 25 items and the avg selling price is $1200. We can find the total sum by multiplying it out. The total sum of the 25 items are $30000.

The question states that no item was sold for less than $420 and EXACTLY 10 items sold for less than 1000. So, to maximize the highest selling item, we can choose the price of $420 for all 10 of those items that sold for less than 1000. This would total $4200.

So, that leaves us with 15 items left to find values for. If the next 14 items sold for $1000 each (since it satisfies the constraint of each item being greater than $420 and the 10 items <1000 are accounted for) thus totalling $14000.

The highest price of the most expensive item, therefore will be $30000 - $14000 - $4200 = $11,800.

Hi all,

I was working on some Quant problems from my Kaplan book and had a question about one question. I was wondering about the best and simplest way to solve this kind of a problem. Also, does this sound like a medium or difficult question ?

Q) At an auction, a line of 25 items were sold with an average price of $1200. If none of the items were sold for less than $420 and exactly 10 items were sold for less than $1000, what is the greatest possible selling price of the most expensive product ?

A) 2600
B) 3900
C) 7800
D) 11800
E) 18200

extremely well done.

two general takeaways to be had here.
first, there's the principle that actually applies to this problem:
(1) if you want to maximize something, try minimizing everything else.
and, of course, there's...
(2) if you want to minimize something, try maximizing everything else.