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09 Apr 2025, 21:49
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Highest: Yellow
Lowest: Orange
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
58% (03:28) correct
42%
(03:23)
wrong
based on 146
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In a regional darts challenge, the board is divided into six color zones: Red, Orange, Yellow, Green, Blue, and Violet. Each color gives a unique even number of points between 2 and 12, inclusive. Players throw exactly three darts. To qualify for the next round, a score of at least 22 is required.
The following facts are known:
- One player scored exactly 18 with Red, Green, and Violet and did not qualify.
- A different player scored exactly 24 with Orange, Yellow, and Blue and just qualified.
- The value of Green is exactly 2 more than Violet.
- Red is worth 4 times more than Orange.
- Blue is worth less than Yellow.
Based on the following information, select for Highest the color that gives the most amount of points, and for Lowest the color that gives the least amount of points.
The following facts are known:
- One player scored exactly 18 with Red, Green, and Violet and did not qualify.
- A different player scored exactly 24 with Orange, Yellow, and Blue and just qualified.
- The value of Green is exactly 2 more than Violet.
- Red is worth 4 times more than Orange.
- Blue is worth less than Yellow.
Based on the following information, select for Highest the color that gives the most amount of points, and for Lowest the color that gives the least amount of points.
| Highest | Lowest | |
| Red | ||
| Orange | ||
| Yellow | ||
| Green | ||
| Blue | ||
| Violet |
ShowHide Answer
Official Answer
Highest: Yellow
Lowest: Orange
09 Apr 2025, 22:20
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Bismuth83
Given
six color zones: Red, Orange, Yellow, Green, Blue, and Violet.
six points unique even number of points between 2 and 12, inclusive.
To win : >= 22 pts needed.
Table 1:
18 pts = R+ G+V
to get sum of 18, possible cases are
4,6,8
2,6,10
2,4,12
Table 2:
24 pts = O+ Y+ B
POSSIBLE CASES
10,12,2
10,8,6
12,8,4
Table 3:
G = 2+V
possible cases (G,V)
4,2
6,4
8,6
10,8
12,10
using table 1 cases to compare table 3, (12,10) ; (10,8) are out .
We are left with (G,V) = (4,2);(6,4);(8,6)
if G,V = 4,2 then R = 12
if G,V = 6,4 then R = 8
if G,V = (8,6) then R = 4
using the constraint R = 4* orange
if G,V = 4,2 then R = 12 , then orange =3
if G,V = 6,4 then R = 8. , then orange = 2
if G,V = (8,6) then R = 4 , then orange = 1
So, we know now 18 pts = R+ G+V = 8+ 6+4
and Orange = 2
Now look table 2, the only case with orange 2 is first one.
Table 2:
24 pts = O+ Y+ B
POSSIBLE CASES
10,12,2
10,8,6
12,8,4
Given constraints is Blue less than yellow.
hence, Yellow = 12, Blue =10, orange =2
Greatest is 12 yellow , least is 2= Orange
09 Apr 2025, 22:49
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According to the question,
Each colour represents a UNIQUE EVEN NUMBER between 2 and 12 (inclusive). So, the numbers are 2, 4, 6, 8, 10 and 12. List=[2,4,6,8,10,12]
According to the facts,
1. Red= 4*Orange. This implies that the only number that orange can be is 2 as there is no other number which when multiplied by 4 will be a part of our list. Thus, Red=8 and Orange is 2.
2. The value of Green is exactly 2 more than Violet. Green+Violet+Red=18 (Given)
but from 1. Red=8,
=> Green+Violet=10.
The only two consecutive numbers that fit the criteria are 4 and 6. Hence, Green=6 and Violet=4.
3. Now, we have two numbers remaining: 10 and 12. Blue is worth less than Yellow (given). Hence, Blue=10 and Yellow=12.
Answer: Highest: Yellow, Lowest: Orange
Each colour represents a UNIQUE EVEN NUMBER between 2 and 12 (inclusive). So, the numbers are 2, 4, 6, 8, 10 and 12. List=[2,4,6,8,10,12]
According to the facts,
1. Red= 4*Orange. This implies that the only number that orange can be is 2 as there is no other number which when multiplied by 4 will be a part of our list. Thus, Red=8 and Orange is 2.
2. The value of Green is exactly 2 more than Violet. Green+Violet+Red=18 (Given)
but from 1. Red=8,
=> Green+Violet=10.
The only two consecutive numbers that fit the criteria are 4 and 6. Hence, Green=6 and Violet=4.
3. Now, we have two numbers remaining: 10 and 12. Blue is worth less than Yellow (given). Hence, Blue=10 and Yellow=12.
Answer: Highest: Yellow, Lowest: Orange
