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

Question

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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Official Answer

C

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

(Inspired by an OG question)

PKN · Answer

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)

sumit411 · Answer

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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Hazel1134 · Answer

Cheapest price Chocolate : x 
Most expensive chocolate: 4x+4

Since the Median price of the chocolate is 20,

Considering we have DISTINCT price for each bar of chocolate, 
we have a set of prices like so: { x, x+1, x+2, 20, 21, 22, 4x+4}

Because we want to have the maximum price, the numbers between the median and the maximum price has to be close to each other, and since the problem states that the prices are in integers, so, closest two numbers to 20 are 21 & 22.

Since the total is 105 cents, subtract 20,21, and 22 first, resulting 42.

Remaining numbers, x, x+1, x+2, 4x+4 are then solved

42 = 7x+7 
x = 5 
> Plug 5 back to 4x+4 and we get 24.

Answer is C

bumpbot · Answer

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

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