I27-23

Question

At toy store, five types of model cars are available, priced as follows: $15, $25, $35, $45, and $55.
 
A group of customers visits the store and makes purchases with the following conditions:
 
- Each customer can buy at least 1 car and at most 3 cars.
 
- A customer cannot buy more than one of each car type.
 
- On average, each model car purchased costs $35.
 
In addition, the group’s total spending is $420.
 
Based on the above information, select for  Maximum  the maximum number of possible people in the group and for  Minimum  the minimum number of possible people in the group.

Bunuel · Answer

Official Solution:

The question asks us to find the limits to the number of possible people in the group.
 
Let’s first analyze the possible car combinations people could’ve bought:
 
• 1 model car: $35. The cost is $35.
 
• 2 model cars: $25 and $45; $15 and $55. The cost is $70.
 
• 3 model cars: $15, $35, and $55; $25, $35, and $45. The cost is $105.
 
For there to be as many people as possible, everyone needs to spend as little as possible - which is buying 1 model car for $35. Likewise, for there to be as few people as possible, everyone needs to spend as much as possible - which is buying 3 model cars for $105.
 
Then, the maximum number of people in the group is equal to  \frac{420}{35} = 12  and the minimum number of people in the group is equal to  \frac{420}{105} = 4 .

Correct answer:

Maximum  "12"

Minimum  "4"

rak08 · Answer

When we say Maximum number of people 
so we can assume that 
420/35 = 12

Minimum 
55+35+15 = 105 
so 3
 why 4

Bunuel · Answer

Because 3 people spending 105 each totals 315, which is less than 420. You need 4 people to reach 420.

adarsh2209 · Answer

I like the solution - it’s helpful.

repellatdeserunt · Answer

I did not quite understand the solution. why cant 28 people each buy 15 dollar cars, this question is confusing. especially the average part. Cannot understand why they mentioned that.

Bunuel · Answer

Read the conditions carefully. We are told that, on average, each model car purchased costs $35, and the group’s total spending is $420. With this in mind, how can there be 28 people each buying $15 cars? The average would be $15, not $35. If this is still not clear, please check alternative solutions here: https://gmatclub.com/forum/at-toy-store ... 38814.html

Karym · Answer

I like the solution - it’s helpful.

Karym · Answer

I like the solution - it’s helpful.

Thelatebloomer · Answer

I found this answer quite simple to understand:
Since the  average cost per car is $35  and the  total spending is $420 , the total number of cars bought is:
420/35=12

So the group purchased  12 cars in total .
Now use the customer constraints:
 
 Each customer buys  at least 1  car  
 Each customer buys  at most 3  cars  
 No duplicate car type per customer   
 Maximum possible number of people 
To maximize the number of people, each person should buy as few cars as possible:
 
 1 car per person  
 12 total cars   
So:
12 people
This is achievable, for example if all 12 cars are the $35 model.

Minimum possible number of people 
To minimize the number of people, each person should buy as many cars as possible:
 
 3 cars per person  
 12 total cars   
So:
12/3 = 4 people

BrownBearBR · Answer

I like the solution - it’s helpful.

I27-23

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