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Sajjad1994
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A soccer competition consisted of two rounds. In each round, the 20 te 29 Oct 2020, 10:53
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A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
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E
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A soccer competition consisted of two rounds. In each round, the 20 te 29 Oct 2020, 13:59
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Number of teams that won in first round= 20/2 =10

out of those 10 winning teams, number of teams that lost in round 2 = 10-7 =3

Number of teams that won both matches = 10-3 =7


Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
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A soccer competition consisted of two rounds. In each round, the 20 te 29 Oct 2020, 16:43
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Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
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There must be 10 teams that lost once and 10 teams that won once after the first round. For the second round focus on the 10 loser teams, they are playing against the 10 winner teams from the first round. Among the 10 teams that lost once, 7 of them lost again so we have 7 winner teams that won again, hence 7 teams that won twice.

Ans: E
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A soccer competition consisted of two rounds. In each round, the 20 te 05 Nov 2020, 11:20
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Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
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Solution:

In each round, exactly 10 teams win and 10 teams lose. In the second round, exactly 10 teams lost the game; since 7 of these teams also lost the first game, 10 - 7 = 3 of the teams must have won their first game. Thus, the number of teams that won the first game but lost the second game is 3. Since 10 teams won the first game and 3 of these teams lost the second game, the remaining 10 - 3 = 7 teams won both games.

Answer: E
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A soccer competition consisted of two rounds. In each round, the 20 te 13 Apr 2025, 05:53
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didn't get this why do we have to take exact 10 why not 8 or 9 and also can't understand how the calculation work in this.
ScottTargetTestPrep
Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
Solution:

In each round, exactly 10 teams win and 10 teams lose. In the second round, exactly 10 teams lost the game; since 7 of these teams also lost the first game, 10 - 7 = 3 of the teams must have won their first game. Thus, the number of teams that won the first game but lost the second game is 3. Since 10 teams won the first game and 3 of these teams lost the second game, the remaining 10 - 3 = 7 teams won both games.

Answer: E
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A soccer competition consisted of two rounds. In each round, the 20 te 13 Apr 2025, 07:17
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shubhim20
didn't get this why do we have to take exact 10 why not 8 or 9 and also can't understand how the calculation work in this.
ScottTargetTestPrep
Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
Solution:

In each round, exactly 10 teams win and 10 teams lose. In the second round, exactly 10 teams lost the game; since 7 of these teams also lost the first game, 10 - 7 = 3 of the teams must have won their first game. Thus, the number of teams that won the first game but lost the second game is 3. Since 10 teams won the first game and 3 of these teams lost the second game, the remaining 10 - 3 = 7 teams won both games.

Answer: E
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We have to take exactly 10 because in each round there are 20 teams playing in 10 matches - so exactly 10 teams win and 10 teams lose (since there are no ties).

In Round 2, 10 teams lost. Out of those, 7 had already lost in Round 1.

That means the other 3 teams who lost in Round 2 must have won in Round 1.

So, out of the 10 teams that won in Round 1, 3 lost in Round 2 - leaving 10 - 3 = 7 teams who won both games.

That’s how the calculation works - it’s always exactly 10 winners and 10 losers per round.
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A soccer competition consisted of two rounds. In each round, the 20 te 20 Nov 2025, 20:08
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For anyone less math-savvy like myself, this problem was surprisingly simple. I just used some logic:

"Of those who lost the first round, 7 also lost the second round." => 7 teams lost both round 1 and round 2. At least 7 teams lost in the first round, too.

"How many teams won both games?"

Think about how competitions work!

"None of the games resulted in a tie." => that means every team won, or lost.

If 7 teams lost in the second round, that means 7 other teams (the ones the losers competed against) won in that second round.

If those same 7 teams lost both times, it's a logical step to infer that 7 other teams also won both rounds, since every loss also has a win.

That's all I used to complete this problem. Sure, you can call it a stretch without the underlying, precise math (you could argue at least one of those other teams lost round one but won round two, or vice versa), but the time saved was a worthwhile risk for me.


Sajjad1994
A soccer competition consisted of two rounds. In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single game. None of the games resulted in a tie, and of the teams that lost in the first round, 7 also lost in the second round. How many teams won both of their games?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7
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