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Jacob purchased 7 chocolates, price of each of these 7 chocolates is a

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Jacob purchased 7 chocolates, price of each of these 7 chocolates is a  [#permalink]

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New post 18 Aug 2018, 09:26
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (03:15) correct 50% (02:23) wrong based on 22 sessions

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Jacob purchased 7 chocolates, price of each of these 7 chocolates is an integer number of cents, and all prices are distinct. Average price of these 7 chocolates is 15 cents, and median price is 20 cents. If the price of the most expensive chocolate is 4 cents more than 4 times the price of the cheapest chocolate, what is the maximum possible price of the most expensive chocolate, in cents?

A. 22
B. 23
C. 24
D. 25
E. More than 25



(Inspired by an OG question)
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Jacob purchased 7 chocolates, price of each of these 7 chocolates is a  [#permalink]

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New post 18 Aug 2018, 10:11
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amanvermagmat wrote:
Jacob purchased 7 chocolates, price of each of these 7 chocolates is an integer numberof cents, and all prices are distinct. Average price of these 7 chocolates is 15 cents, and median price is 20 cents. If the price of the most expensive chocolate is 4 cents more than 4 times the price of the cheapest chocolate, what is the maximum possible price of the most expensive chocolate, in cents?

A. 22
B. 23
C. 24
D. 25
E. More than 25

(Inspired by an OG question)


Say, x is price of the cheapest chocolate and x is an integer.

Given, the price of the most expensive chocolate is 4 cents more than 4 times the price of the cheapest chocolate.
Or, the price of the most expensive chocolate=4x+4
To find:- 4x+4=?

Observation:- Eliminate the answer options A,B, and D as these aren't in the form of 4x+4.

Option-C:-
4x+4=24, hence x=5
So, the set of price of chocolates could be: {5,6,7,20,21,22,24}
Keep it.

Option E:- Price of chocolate more than 25, in the form 4x+4 is 28. Or, x=6
Price of the 7 chocolates :-
6, a, b, 20, c, d,28
Since 28 is the maximum value, hence
1) a and b has to be minimum ,distinct, greater than 'x' , and less than the median value.
2) c and d has to be minimum ,distinct, less than '4x+4', and greater than median.
So, a and b could be 7 and 8 respectively.
& c and d could be 21 and 22 respectively.
Hence, total price of chocolates=6+7+8+20+21+22+28=112
Given, Total price of the chocolates=Average price*7=15*7=105
So, the price of the most expensive chocolate can't be more than 25. Eliminate E.

Ans. (C)
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Re: Jacob purchased 7 chocolates, price of each of these 7 chocolates is a  [#permalink]

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New post 18 Aug 2018, 11:36
1
C

Sum of all =15*7=105

Now we want to minimize the other cost as we are looking for maximum possible cost

y, y+1, y+2, 20, 21, 22, 4+4y

Solving for sum =105
y = 5
Therefore x= 24

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Re: Jacob purchased 7 chocolates, price of each of these 7 chocolates is a &nbs [#permalink] 18 Aug 2018, 11:36
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