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18 Dec 2023, 07:00
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3: x
5: Highest Rating
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
In this digital world of the food market, a simple 5-point rating system holds immense weight. Ratings often act as primary filters, helping to narrow down choices and offering an immediate snapshot of a restaurant's performance.
On a particular day, two restaurants got exactly five ratings as given in the table. The ratings were given out of digits 1 to 5, where the Range is the difference between the largest and smallest value. The Mean is the average of the five ratings, while the Median is the center value when the values are placed in ascending/descending order, and the Mode is the value that appears the maximum number of times.
(Sort ↕ the table by clicking on the headers)
Based on the above information and preceding tables, select for x the range of ratings that Dumb Pizza got and for Highest rating the maximum rating that Pizza King could have got
Improved version of this question is HERE.
|
In this digital world of the food market, a simple 5-point rating system holds immense weight. Ratings often act as primary filters, helping to narrow down choices and offering an immediate snapshot of a restaurant's performance.
On a particular day, two restaurants got exactly five ratings as given in the table. The ratings were given out of digits 1 to 5, where the Range is the difference between the largest and smallest value. The Mean is the average of the five ratings, while the Median is the center value when the values are placed in ascending/descending order, and the Mode is the value that appears the maximum number of times.
| Statistical Data | Dumb Pizza | Pizza King |
|---|---|---|
| Mean | 3.2 | 3.4 |
| Median | 2 | 3 |
| Mode | 2 | 3 |
| Range | x | 3 |
Based on the above information and preceding tables, select for x the range of ratings that Dumb Pizza got and for Highest rating the maximum rating that Pizza King could have got
Improved version of this question is HERE.
| x | Highest Rating | |
| 3 | ||
| 5 |
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Official Answer
3: x
5: Highest Rating
18 Dec 2023, 07:13
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In this digital world of the food market, a simple 5-point rating system holds immense weight. Ratings often act as primary filters, helping to narrow down choices and offering an immediate snapshot of a restaurant's performance.
On a particular day, two restaurants got exactly five ratings as given in the table. The ratings were given out of digits 1 to 5, where the Range is the difference between the largest and smallest value. The Mean is the average of the five ratings, while the Median is the center value when the values are placed in ascending/descending order, and the Mode is the value that appears the maximum number of times.
(Sort ↕ the table by clicking on the headers)
Based on the above information and preceding tables, select for x the range of ratings that Dumb Pizza got and for Highest rating the maximum rating that Pizza King could have got[/quote]
Dumb Pizza : -
Mean = 3.2; Total ratings = 3.2 *5 = 16
Median = 2; Mode = 2; Range = x
Ratings in increasing order for Dumb Pizza = {2,2,2,5,5}
The range of ratings that Dumb Pizza got = 5 - 2 = 3
Pizza King: -
Mean = 3.4; Total ratings = 3.4 *5 = 17
Median = 2; Mode = 2; Range = 3
Ratings in increasing order for Dumb Pizza = {2,3,3,4,5}
The maximum rating that Pizza King could have got = 5
On a particular day, two restaurants got exactly five ratings as given in the table. The ratings were given out of digits 1 to 5, where the Range is the difference between the largest and smallest value. The Mean is the average of the five ratings, while the Median is the center value when the values are placed in ascending/descending order, and the Mode is the value that appears the maximum number of times.
| Statistical Data | Dumb Pizza | Pizza King |
|---|---|---|
| Mean | 3.2 | 3.4 |
| Median | 2 | 3 |
| Mode | 2 | 3 |
| Range | x | 3 |
Based on the above information and preceding tables, select for x the range of ratings that Dumb Pizza got and for Highest rating the maximum rating that Pizza King could have got[/quote]
Dumb Pizza : -
Mean = 3.2; Total ratings = 3.2 *5 = 16
Median = 2; Mode = 2; Range = x
Ratings in increasing order for Dumb Pizza = {2,2,2,5,5}
The range of ratings that Dumb Pizza got = 5 - 2 = 3
Pizza King: -
Mean = 3.4; Total ratings = 3.4 *5 = 17
Median = 2; Mode = 2; Range = 3
Ratings in increasing order for Dumb Pizza = {2,3,3,4,5}
The maximum rating that Pizza King could have got = 5
General Discussion
18 Dec 2023, 07:45
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First let's look into dumb pizza :
Sum of reviews is 16
2 is median and mode so 2 is minimum 2 times.
2,2,x,y,z
x should either be 2 or greater than 2 for the sum to be 16.But in that case it wont remain the median so x=2
this leaves y and z =5 each making the range as 3 which is x.
For pizza king:
Sum is 17
3 is median and we want to see if a maxima of 5 is possible it is if we give 2 3's and a rating of one 2 one 4 and one 5 the above conditions for pizza king is satisfied including the range. so 5 is the maxima in this case.
Sum of reviews is 16
2 is median and mode so 2 is minimum 2 times.
2,2,x,y,z
x should either be 2 or greater than 2 for the sum to be 16.But in that case it wont remain the median so x=2
this leaves y and z =5 each making the range as 3 which is x.
For pizza king:
Sum is 17
3 is median and we want to see if a maxima of 5 is possible it is if we give 2 3's and a rating of one 2 one 4 and one 5 the above conditions for pizza king is satisfied including the range. so 5 is the maxima in this case.
