A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, a

Question

A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 runs. They lost by one run in exactly five games. In each of the other games, they scored twice as many runs as their opponent. How many total runs did their opponents score?

(A) 35
(B) 40
(C) 45
(D) 50
(E) 55

(A) 35
(B) 40
(C) 45
(D) 50
(E) 55

EgmatQuantExpert · Answer

Solution 
  Given:  
 • A softball team played ten games, scoring 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 runs. 
• The team lost by one run in exactly five games. 
• In each of the other games, the team scored twice as many runs as their opponent.

To find:  
 • The total runs scored by the opponent team.

Approach and Working:  
As in 5 games, the team scored twice of their opponent’s score, those 5 scores must be 2, 4, 6, 8, and 10 (as twice a number must be even).
 • Hence, in those 5 games, the total score of the opponent = 1/2 (2 + 4 + 6 + 8 + 10) = 15

Also, in the remaining each of the 5 games, the team scored 1 less than the opponent.
 • Hence, in the remaining 5 games, the total score of the opponent = (1 + 3 + 5 + 7 + 9) + 5 = 30
• Therefore, total score of the opponent team = 15 + 30 = 45

Hence, the correct answer is option C.

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

eswarchethu135 · Answer

As they scored twice the score of the opponents in five games. The scores must be even numbers as odd numbers can't come if we multiply by 2.

So the five scores are 2,4,6,8,10. The opponent scores in 5 games are 1,2,3,4,5.

In the rest 5 games, they lost by 1 run in each game. So the opponent scores are 2,4,6,8,10.

The opponent sum of scores is 1+2+3+4+5+2+4+6+8+10 = 45

OPTION:  C

Archit3110 · Answer

total score of team ; 10*11/2 ; 55
for half of matches opponents score +1 extra ; 5 runs
and for 5 matches team score ; 5*2 ; 10 extra
so difference 10 less will be opponent score ; 55-10 ; 45
IMO C

saukrit · Answer

If in 5 games they scored exactly twice(2*X), then in these games they score score which was even. Hence the five games in which the softball team score twice, their scores were:  2,4,6,8,10

In the same 5 games the score of the opponent team were half. Hence in these 5 games the opponent scores were :    1,2,3,4,5     (dividing each score above by 2)

In the remaining 5 games the score of softball team was:  1,3,5,7,9 (all remaining odd scores) 
In these games the team score 1 less than opponents, hence, Opponent team's scores were :    2,4,6,8,10    (adding 1 to each score above)

The total score of opponent team =  2+4+6+8+10+1+2+3+4+5 = 45 
  
  Hence, Answer is C

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