A certain number of people visited an amusement park on a specific day

Question

A certain number of people visited an amusement park on a specific day, which featured three rides: the Ferris Wheel, Classic Wooden Rollercoaster, and Merry-Go-Round, costing $1, $2, and $3 per ride, respectively.

Each person spent an average of $2 per ride, and the total money spent was $120. Every person took at least one ride and did not repeat any ride.

Based on this information, select for  Maximum  the greatest possible number of visitors and for  Minimum  the smallest possible number of visitors who could have visited the park.

Bunuel · Accepted Answer

Official Solution: Each person spending an average of $2 per ride implies the following three scenariois: • A person could have taken all three rides ($1 + $2 + $3 = $6 total), resulting in an average of $2 per ride. • A person could have taken the $1 and $3 rides ($1 + $3 = $4 total), again averaging $2 per ride. • A person could have taken only the $2 ride. Since the total spending was $120, the minimum number of people occurs when the maximum spending per person ($6) is achieved. This results in 120/6 = 20 people, meaning all 20 people took each of the three rides once. Conversely, the maximum number of people occurs when the minimum spending per person ($2) is achieved. This results in 120/2 = 60 people, meaning all 60 people took only the $2 ride once. Correct answer: Maximum "60" Minimum "20" GMAT-Club-Forum-5ggs3tsk.png

Bismuth83 · Answer

1. First let's analyze the problem. "Each person spent an average of $2 per ride" means that each person did one of the following combinations: $1 and $3 rides; $2 ride; $1, $2, and $3 rides.

2. The total amount of money spent is $120. The smallest number of possible visitors happens when everyone spends as much as possible. In this case, it would be when everyone goes on $1, $2, and $3 rides together - or spending $6 each. Then, the number of visitors would be  \frac{120}{6} = 20 .

3. Now the largest number of possible visitors happens when everyone spends as little as possible. In this case, it would be when everyone goes on $2 rides - or spending $2 each. Then, the number of visitors would be  \frac{120}{2} = 60 .

4. Our answer will be:   Maximum - 60 and Minimum - 20  .

satavishamitra · Answer

I'm confused about a point. So, average amount spent by each visitor = $2. 
I get that max amount spent could be $6.
But why the minimum amount spent by each visitor can't be $1?

Bunuel · Answer

The minimum amount spent per visitor  cannot be $1  because the question states that the  average amount spent per ride is $2 .

pratikshyasuar · Answer

"Each person spent an average of $2 per ride"
There are 2 ways this can be interpreted:
1. total money spent/ total rides=2 
or
2. any given person took either 
 a. 1 ride (roller coaster), average= $2/1ride = $2
 b. 2 rides (ferris wheel and merry go round), average= $(1+3)/2rides = $2
 c. all 3 rides, average=$(1+2+3)/3 rides= $2
The sentence mixes individual words with a group math formula, pulling your brain in two opposite directions:
The English Grammar View (Interpretation 2): Because the sentence starts with "Each person," our brains naturally look at the visitors one by one. In everyday speech, if you say, "Each person bought an average of $2 worth of candy," it sounds like every single individual walked away with exactly $2 worth of sweets. Nobody spent $0.50, and nobody spent $5.

The Math Class View (Interpretation 1): In word problems, an "average per ride" is a locked group formula: Total Money/Total Rides. In this view, "Each person" is just a generic placeholder word used to describe the whole crowd's average rate, without actually banning individuals from making different choices.

While both interpretations happen to yield the same answer (Min 20, Max 60) due to the symmetry of the dataset ($1, $2, $3 with a target average of $2), they do not yield the same result if we change the values.

Proof that they diverge:
If the ride costs were $1, $2, and $5 with a target average of $3 per ride (Total spent = $120):

Interpretation 1 (Group Average): Total rides = $120 / $3 = 40 rides. To maximize people, we give everyone 1 ride. We can mix and match visitors across the park (e.g., 20 people on the $5 ride, 20 people on the $1 ride) to achieve a maximum of 40 people.

Interpretation 2 (Individual Constraint): Every single person must average exactly $3. No single ride costs $3, and the 3-ride combo averages $2.66. The only valid individual option is the 2-ride combo ($1 + $5 = $6 total). This locks the maximum headcount at $120 / $6 = 20 people.

Since the two paths diverge with different data, the question stem should be updated to match the official solution's logic.

Suggested wording change:
"Every individual visitor maintained a personal average expenditure of $2 per ride for the specific rides they selected."
"For each personal combination of rides, the average cost per ride was $2."
"Each person chose a set of rides such that their average expenditure was $2 per ride."

A certain number of people visited an amusement park on a specific day

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A certain number of people visited an amusement park on a specific day

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