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The Tigers beat the Sharks 2 out of the first 3 times they played. The

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The Tigers beat the Sharks 2 out of the first 3 times they played. The  [#permalink]

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New post 18 Mar 2019, 10:02
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The Tigers beat the Sharks 2 out of the first 3 times they played. They then played N more times, and the Sharks ended up winning at least 95% of all the games played. What is the minimum possible value for N?

(A) 35
(B) 37
(C) 39
(D) 41
(E) 43
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Re: The Tigers beat the Sharks 2 out of the first 3 times they played. The  [#permalink]

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New post 18 Mar 2019, 10:38
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Noshad wrote:
The Tigers beat the Sharks 2 out of the first 3 times they played. They then played N more times, and the Sharks ended up winning at least 95% of all the games played. What is the minimum possible value for N?

(A) 35
(B) 37
(C) 39
(D) 41
(E) 43


Currently the winning percent of Sharks is 1/3*100= 33.33 %.Since we have to find the minimum possible value of N for which Shark's winning percentage becomes at least 95% . So sharks has to win all the N matches so that N is minimized.

Hence total matches = N+3. When shark will have winning percent of 95% then that of tigers will be 5%. And they will win only total of 2 matches

So 2 matches correspond to 5% of the total matches.
Therefore total number of matches = 2/5*100 = 40.

So N+3 = 40 => N= 37

Alternatively, you can solve the following equation and find the answer .

2/(N+3) = 5/100

Solving you will get N = 37. Hence B)
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Re: The Tigers beat the Sharks 2 out of the first 3 times they played. The  [#permalink]

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New post 28 Feb 2020, 00:00
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Noshad wrote:
The Tigers beat the Sharks 2 out of the first 3 times they played. They then played N more times, and the Sharks ended up winning at least 95% of all the games played. What is the minimum possible value for N?

(A) 35
(B) 37
(C) 39
(D) 41
(E) 43


Solution:


    • Tiger beats sharks in 2 out of the first 3 matches.
    • Sharks ended up winning at least \(95\%\) matches
      o Sharks lose at most \(5\%\) match
    • Now, total matches = \(N+3\)
      o For the minimum number of matches, we can assume that sharks lost only 2 matches
    • By above inferences
      o \(2 ≤ 5\%\ of\ (N+3)\)
      o \(2 ≤\frac{5}{100}*(N+3)\)
      o \(2 ≤ \frac{1}{20}*(N+3)\)
      o \(40 ≤ N+3\)
      o \(40-3 ≤ N\)
      o \(37 ≤ N\)
    • The minimum possible value of N is 37.
Hence, the correct answer is Option B.
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Re: The Tigers beat the Sharks 2 out of the first 3 times they played. The  [#permalink]

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New post 28 Feb 2020, 00:32
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total game played among them= N+3

game won by sharks = N+3-2

(because we have to minimize the total no. of games....so assume that all other games were won by sharks...)

given...N+1/N+3 * 100 = 95

N= 37..

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Re: The Tigers beat the Sharks 2 out of the first 3 times they played. The  [#permalink]

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New post 28 Feb 2020, 00:46
Initial 3 matches, tiger wins 2 and shark wins 1, so if they play n more matches
Total matches =n+3
As we have to consider minimum value it is possible when shark losses no further match
So lost match by shark = 2 which is 5% of total matches played
I.e. 2=5%x (X is total matches played n+3)
=40
N=37

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Re: The Tigers beat the Sharks 2 out of the first 3 times they played. The   [#permalink] 28 Feb 2020, 00:46
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