I07-03

Question

Donnie’s Donuts delivers donuts by the dozen (12 per dozen) to five businesses: Fred’s Flowers, Greg’s Garage, Harold’s Chicken, John’s Juices, and Kenny’s Kitchen. Each day, Donnie delivers exactly 120 donuts. The orders are as follows: Fred’s Flowers and Greg’s Garage each order 2 dozen donuts per day, John’s Juices and Kenny’s Kitchen each order 3 dozen donuts per day, and Harold’s Chicken orders 5 dozen donuts per day. 
 
During a certain 3-day period, each business placed at least one order, and no business placed more than two orders. 
 
Select for  Highest  the highest total number of donuts a single business purchases in this period and select for  Lowest  the lowest total number of donuts a single business purchases in the same period.

Rashmi96 · Accepted Answer

I don’t quite agree with the solution. least number of order should be 1 order by F or G, 2dozen=24 donut, why are we considering 2 orders of F or G, the question says, atleast 1 order , kindly explain

Bunuel · Answer

Official Solution:

Let's simplify and calculate in dozens. The orders per business are as follows:
  
• F = 2
 
• G = 2
 
• J = 3
 
• K = 3
 
• H = 5
   
Since exactly 10 dozens are delivered each day, the following five sets of deliveries, each totaling 10 dozens, are possible:
  
• {F, G, J, K} = 10
 
• {H, F, J} = 10
 
• {H, F, K} = 10
 
• {H, G, J} = 10
 
• {H, G, K} = 10
  
Notice that all three days cannot use a set with three businesses because each such set includes H, and no business places more than two orders. Therefore, one of the days must use {F, G, J, K}, and the other two days must use triplets that ensure each business places at least one order. This can be achieved with the following distribution over the three days: {F, G, J, K}, {H, F, J}, and {H, G, K}. With this, we find that each business receives exactly two orders over the three-day period.
 
Therefore, the highest total number of donuts purchased by a single business is for H, totaling 5 + 5 = 10 dozens = 120 donuts. The lowest total is for F or G, each totaling 2 + 2 = 4 dozens = 48 donuts.

Correct answer:

Highest  "120"

Lowest  "48"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

charlie1195 · Answer

I like the solution - it’s helpful.

Bunuel · Answer

The question says  "each business placed at least one order"  and  "no business placed more than two orders."

That means the  minimum  number of orders per business is 1, and the  maximum  is 2. But we also know the total number of donuts delivered is  120 per day * 3 days = 360 donuts .

If  F  or  G  placed only  1 order  (i.e., 24 donuts), we would not be able to distribute the remaining donuts to other businesses  while also ensuring every business places at least one order and no more than two .

That’s why the solution checks valid combinations of daily deliveries totaling 120 donuts, while satisfying all constraints. The only workable distribution is the one where  each business places exactly 2 orders , meaning  F and G each receive 48 donuts , not 24.

Please review the question and the solution carefully.

idlch · Answer

I like the solution - it’s helpful.

Edwin555 · Answer

I like the solution - it’s helpful. This is a really good question!

Confusion · Answer

So basically the question is not asking max or least for 1 day but across the 3 days?

Bunuel · Answer

Yes, it’s about the total over the 3 days for each business, not just one day.

srik410 · Answer

Kind of confusing wording. But let me take a crack at it.

F G H J K are 2 2 5 3 3 which sum up to 15. Given three days with 10 dozen orders per day. So in total 30 orders needed to be served.
Seems to me that 2*15 = 30 ie 2 *(F G H J K) fits here. ie if I take 2 of each with some pairings each day(which I don't care how), it would fit all the conditions.

Since we have to use any type atleast once and max twice, there is no way to replace one with another. For example you want to come up with the same sum 30 over 3 days, how can you split 2*(F G H J K) into other combinations? There is no way(since we can only afford max 2 of any kind).

Finally, the question is max count ordered by any single business. Not in any single day. So, we cannot care less about the ordering each day. We know every business ordered twice.

So, max=2*H=120 and min =2*F or 2*G=48

Paattaa · Answer

This is a great question that’s helpful for learning.

SanketPatil · Answer

I did not quite understand the solution. Framing of question is not clear

Bunuel · Answer

Check alternative solution here: https://gmatclub.com/forum/donnie-s-don ... l#p3493552

Advait01 · Answer

I like the solution - it’s helpful.

I07-03

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