I29-137

Question

Five robotics teams recorded integer scores across five rounds. Two scores were lost: Bolt’s Round 3 score (denoted x) and Echo’s Round 5 score (denoted y).
 
 Facts known about the missing values: 
    There were no ties in any round or in the final total scores. 
 Bolt finished in a different position in each of the five rounds. 
 y is the median of Echo’s five round scores.         Team     Round 1     Round 2     Round 3     Round 4     Round 5     Total       Atlas  22  35  21  31  19  128     Bolt  38  40  x  27  18  123 + x     Circuit  25  29  39  24  27  144     Drift  31  41  11  36  22  141     Echo  28  33  25  32  y  118 + y     
The placement of x, y, 123 + x, and 118 + y in their respective columns when the table is sorted does not provide any information about the actual values of x or y.
 
For each of the following statements, select  True  if the statement is true based on the information provided. Otherwise, select  False .

Bunuel · Answer

Official Solution:

• In Round 5, the highest score is achieved by Echo. 
 
Without y, Echo’s scores in ascending order are {25, 28, 32, 33}. Since y is the median, y must satisfy 28 ≤ y ≤ 32. Any of these values would guarantee Echo to win Round 5.
 
Answer:  True 
 
 • Bolt’s total score is greater than Circuit’s total score. 
 
Since Bolt had to finish in a different position in each of the five rounds, and in Rounds 1, 2, 4, and 5 he already took 1st, 2nd, 4th, and 5th places, in Round 3 he must have been 3rd. That forces x to be strictly between 21 and 25. Because no ties are allowed, x can only be 22, 23, or 24. This makes Bolt’s total equal to 123 + x = 145, 146, or 147. Circuit’s total is 144. Thus Bolt’s total is always greater than Circuit’s total.
 
Answer:  True 
 
 • If Bolt got the highest total score, then Echo scored 28 points in Round 5. 
 
Bolt’s variable x can be 22, 23, or 24, giving Bolt totals of 145, 146, or 147.
 
Echo’s variable y can be 28, 29, 30, 31, or 32, giving Echo totals of 146, 147, 148, 149, or 150.
 
For Bolt to win the championship, his total must be 147 while Echo’s total is 146. This happens only when x = 24 and y = 28. Therefore, if Bolt got the highest total score, Echo’s Round 5 score must have been 28.
 
Answer:  True

Correct answer:

In Round 5, the highest score is achieved by Echo.  "True"

Bolt’s total score is greater than Circuit’s total score.  "True"

If Bolt got the highest total score, then Echo scored 28 points in Round 5.  "True"

3D · Answer

This is a great question that’s helpful for learning and I like the solution - it’s helpful.

devdattakhoche · Answer

Bunuel

Here why was Echo have 28 ?

What I perceived from the facts is that :
There were no ties in any round or in the final total scores.

if there were no ties.. we can't have y=28 , is Echo already has 28 as a score in one of the rounds ?

What am I missing ?

Bunuel · Answer

Echo can have 28 twice. We are told that "There were no ties in any round or in the final total scores", which means the "no ties" rule applies only between teams in the same round, not within Echo’s own five scores.

devdattakhoche · Answer

Got you!

Thanks a lot for this !

I29-137

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My Rewards

Team	Round 1	Round 2	Round 3	Round 4	Round 5	Total
Atlas	22	35	21	31	19	128
Bolt	38	40	x	27	18	123 + x
Circuit	25	29	39	24	27	144
Drift	31	41	11	36	22	141
Echo	28	33	25	32	y	118 + y

True	False
		In Round 5, the highest score is achieved by Echo.
		Bolt’s total score is greater than Circuit’s total score.
		If Bolt got the highest total score, then Echo scored 28 points in Round 5.