At toy store, five types of model cars are available, priced as follow

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 · Accepted 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"

itsyodaa · Answer

took little over 4 min, but this question was good..
for finding maximum number of people=
assume, each person bought only 1 car of 35$ so total people=> 420/35=12(max people)
for finding min people consider each people bought 3 car, of total price= 35*3=$105 , 35 is the avg of 3 cars . so each people bought 105 $ worth of car, so total no people => 420/105 = 4

Note: To maximize the no of people we need to minimize the spending. same goes vice versa for minimun

PriyankaGmatIMD · Answer

poojaarora1818 · Answer

I have the answer, but it would be great if you could walk us through the solution.

Ilanchezhiyan · Answer

Minimum:
3 people * 3 different cars = 3(35+45+55) = 405 ___(1)
1 person * 1 car = 15 __ (2)
(1)+(2) =>minimum 4 persons.

Maximum:
12* 35 = 420.

GMAT2025HJ · Answer

Minimum:
3 people * 3 different cars = 3(35+45+55) = 405 ___(1)
1 person * 1 car = 15 __ (2)
(1)+(2) =>minimum 4 persons.

Condition :  On average, each model car purchased costs $35.

avg. in above is $ 42..

Bismuth83 · Answer

1. The question asks us to  find the limits to the number of possible people in the group .

2. 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.

3. 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.

4. 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.

5. Our answer will be:   Maximum - 12 and Minimum - 4  .

jamiedimonn · Answer

KarishmaB  how is the minimum 4?

could you please explain in simple. Please

KarishmaB · Answer

The group's total spending is $420 and average price of each car is $35. 
So 420/35 = 12 cars were bought

Since each customer can purchase at most 3 cars and we want to minimize the number of customers in the group, each person should have bought 3 cars in this case. 
We will need 4 people to buy 12 cars - such that each person buys 3 cars. 
Each could have bought cars of cost $25, $35 and $45 such that average remains $35.

Select  4 for Minimum

To maximize, let each person buy 1 car of $35. So we could have 12 people buying 12 cars.

Select  12 for Maximum

At toy store, five types of model cars are available, priced as follow

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GMAT Two-part Analysis (TPA) Questions

At toy store, five types of model cars are available, priced as follow

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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