Five robotics teams recorded integer scores across five rounds.

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 · Accepted Answer

• 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

I29-137

ODST117 · Answer

Statement 1  - We know  y  is the median of Echo's scores. Sorting Echo's scores in ascending order would give us  25 ,  28 ,  y ,  32 ,  33 . Therefore,  28 <= y <= 32 . Any value of  y  would be the greatest score of round 5. -   True

Statement 2  - The question stem says "There were no ties in any round or in the final total scores" and "Bolt finished in a different position in each of the five rounds". If we look at round 1, Bolt finished in 1st place. For round 2, bolt in 2nd place. For round 4, Bolt in 4th place and for round 5, Bolt in 5th place. Therefore, in round 3, Bolt has to be in 3rd place. In round 3, the 2nd place is  25  points and 4th place is  21  points. Therefore  21 < x < 25 . Possible values for  x =   22 ,  23 ,  24 . Taking the lowest possible value for  x , i.e,  x = 22 , Bolt's total score is  123+22 = 145 , which is greater than Circuits total score of  144 . -   True

Statement 3  - At this point, we know  21 < x < 25  and  28 <= y <= 32 . For Bolt's total score to be the highest, no other total score should be greater than Bolts. If  y = 28 , then Echo's total score is  146 . For Bolt to beat that score and be the highest,  x  needs to be  24 , bringing Bolt's total to  147 . So when Bolt's total score is the highest, i.e, 147, then  y  can only be  28  (because if  y  was greater, it would make Echo's total score the highest). -   True

Dereno · Answer

Let’s first take a look at BOLTs position in each of the rounds.

Round 1: Pos 1

Round 2: Pos 2

Round 3: _____

Round 4: Pos 4

Round 5: _____

For Round 3, 39, 25, X, 21,11 (Pos 3)

39, 25, 21, 11, and X. (Pos 5).

For pos 3, x can hold values 24,23,22 only.

For pos 5, X can hold values less than 11 from 10 onwards till 1.

Round 5, has the values 27,22,19,18 and y.

Given that y is the median value of echo scores. So, 33,32, y, 28 and 25.

So, Y being the median, the values of y are : 31,30,29 only.

If Round 5 value of y = 31/30/29 then the value of Bolts score is 18. Arranging the scores in ascending order, we get

31/30/29 , 27, 22, 19,  18 ( score of Bolt = POS 5).

Hence, X can assume pos 3 in Round 3:

39, 25,  X  , 21, 11.

Question 1: Round 5, the highest score is achieved by Echo.

The round 5 scores are : 27,22,19,18 and y.

And, we have found out that y should be any value within 31,30,29.

It’s clear that any value of Y, will give Echo the highest score. Hence,  True.

Question 2: Bolt’s total score is greater than Circuit’s total score.

Circuits total score = 144

Bolts total score = 123 + X

= 123+24 = 147 (Highest possible value)

= 123+23 = 146

= 123+22 = 145.

Clearly all three values (147,146,145) are greater than 144. Hence,  True.

Question 3: If Bolt got the highest total score, then Echo scored 28 points in Round 5.

The Highest score of Bolt = 147, then echo 118+y can be only among the three values (149,148,147). And, 147 being the lowest score of Echo.

So, Bolt cannot get the highest score. So, the value of Echo cannot be 28 points. Hence,  True .

mayankkamal999 · Answer

1.

The values of Echo in ascending order are 25, 28, 32, 33
As given " y is the median of Echo’s five round scores" the median should be between 28 and 32  
 Hence y is between 28 and 32. 28 <= y <= 32. So, y could be {28,29,30,31,32} 
 In Round 5 highest score is 27 which is below lowest values of y 
 Hence  TRUE

2. 
In Round 1 bolt finished in 1st place
In Round 2 bolt finished in 2nd place 
In Round 4 bolt finished in 4th place 
In Round 5 bolt finished in 5th place (We found that Echo was highest)

Now since " Bolt finished in a different position in each of the five round "
So, In Round 3 Bolt must have finished 3rd place and points of others in ascending order are 11, 21, 25, and 39
Therefore, for Bolt to be 3rd, x should be between 21 and 25
And since there are no ties: 21<x<25
x= {22,23,24}

If x was lowest i.e. 22 then Bolts total score = 123+22=145 which is greater than Circuits score of 144
Hence  TRUE
  
3.
Bolts highest score will be if x is 24. There for highest score= 123+24=147
Now value of y for which Echo's total score is less than 147 
If y=28 then Echo total = 118+28 = 146 which is less than 147
If y=29 then Echo total = 118+29 = 147 which is equal to Bolt's highest score (There can't be any ties)
If y=30 then Echo total will be > Bolts total

Hence it is possible for only y=28
Hence  TRUE

Five robotics teams recorded integer scores across five rounds.

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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.

GMAT Graphs and Tables (G&T) Questions

Five robotics teams recorded integer scores across five rounds.

Prep Toolkit

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