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16 May 2025, 21:54
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Dropdown 1: Car 2
Dropdown 2: Car 7
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (02:18) correct
32%
(02:34)
wrong
based on 639
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In a high-stakes racing competition, each car's performance is evaluated based on a combination of straight-line speed (x-axis) and turn speed (y-axis). The effectiveness of a car on certain racetracks can be ranked using a formula like 5x + 2y, where a higher result indicates better overall performance. The diagram below shows the stats for each car:
Based on the information in the diagram, answer the following questions:
The car with the highest overall performance score using the formula 2x + y is .
The car with the lowest overall performance score using the same formula is .
chart (5).png [ 28.88 KiB | Viewed 3645 times ]
Based on the information in the diagram, answer the following questions:
The car with the highest overall performance score using the formula 2x + y is .
The car with the lowest overall performance score using the same formula is .
Attachment:
chart (5).png [ 28.88 KiB | Viewed 3645 times ]
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Official Answer
Dropdown 1: Car 2
Dropdown 2: Car 7
Updated on: 17 May 2025, 00:13
Originally posted by Aarushi100 on 16 May 2025, 22:46.
Last edited by Aarushi100 on 17 May 2025, 00:13, edited 2 times in total.
Last edited by Aarushi100 on 17 May 2025, 00:13, edited 2 times in total.
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Bismuth83
In this problem,
The car's overall performance is dependent on straight-line speed (x-axis) and turn speed (y-axis). The combination of the two is calculated using a formula 5x+2y.
For dropdown 1:
The formula which is used the calculate the score is given: 2x+y
For highest overall performance score, both x and y must be positive to yield a maximum value of 2x+y.
From the graph we can see that car 2 has the value of x=4 and y=0, which yields 2(4)+0=8.
Similarly, for Car 4 x=2, y=3 which yields 2(2)+3=7.
We can check for all cars, in the positive quadrant but by eyeballing we already know that Car 2 and Car 4 are the only possible contenders and by calculation we have narrowed it down to Car 2.
For dropdown 2:
Again we have to use the same formula: 2x+y.
Here, we adopt the opposite approach.
For lowest overall performance score, both x and y must be negative to yield a minimum value of 2x+y.
From the graph we can see that Car 7 x= -5 , y=-1, yields the minimum value of 2(-5) +(-1) =-11.
Answer:
First Dropdown: Car 2
Second Dropdown: Car 7
17 May 2025, 00:07
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Solution:
Given in the question stem:
1. The X-axis represents the straight-line speed.
2. The Y-axis represents the turn speed.
3. A car's effectiveness can be ranked using the formula 5x + 2y. (This formula represents the overall performance that is evaluated based on a combination of straight-line speed (x-axis) and turn speed (y-axis).)
1. The car with the highest overall performance score using the formula 2x + y is Car 2.
Car 1 = 2(1) + 5 = 7.
Car 2 = 2(4) + 0 = 8 + 0 = 8.
Car 4 = 2(2) + 3 = 4 + 3 = 7.
Car 6 = 2(3) + (-4) = 6 - 4 = 2.
Car 7 = 2(-5) + (-1) = -10 -1 = -11.
2. The car with the lowest overall performance score using the same formula is Car 7.
We have already calculated the car's performance above based on that. And, also by using the same formula, the lowest performance for Car 3 is 2(-1) + (-3) = -5, and Car 8 = 2(-2) + 0 = -4.
Given in the question stem:
1. The X-axis represents the straight-line speed.
2. The Y-axis represents the turn speed.
3. A car's effectiveness can be ranked using the formula 5x + 2y. (This formula represents the overall performance that is evaluated based on a combination of straight-line speed (x-axis) and turn speed (y-axis).)
1. The car with the highest overall performance score using the formula 2x + y is Car 2.
Car 1 = 2(1) + 5 = 7.
Car 2 = 2(4) + 0 = 8 + 0 = 8.
Car 4 = 2(2) + 3 = 4 + 3 = 7.
Car 6 = 2(3) + (-4) = 6 - 4 = 2.
Car 7 = 2(-5) + (-1) = -10 -1 = -11.
2. The car with the lowest overall performance score using the same formula is Car 7.
We have already calculated the car's performance above based on that. And, also by using the same formula, the lowest performance for Car 3 is 2(-1) + (-3) = -5, and Car 8 = 2(-2) + 0 = -4.
Bismuth83
