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A baseball team’s season consists of playing 162 games.

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A baseball team’s season consists of playing 162 games.  [#permalink]

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New post 28 Oct 2018, 02:49
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (02:39) correct 53% (02:27) wrong based on 68 sessions

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A baseball team’s season consists of playing 162 games. At a certain point in its season, the team has won 55 percent of the games it has played. The team then wins a certain number of consecutive games so that at the end of the winning streak, the team has won 58 percent of the games it has played. How many wins did the team have at the end of its winning streak?

a. 10
b. 14
c. 42
d. 77
e. 87
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A baseball team’s season consists of playing 162 games.  [#permalink]

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New post 28 Oct 2018, 03:55
1
There has to be a quicker way than this:

Originally
\(\frac{w}{w+l}\)
55/100
So the options are
11/20, 22/40, 33/60, 44/80, 55/100, 66/120, 77/140, 88/160 and it stops there as a 162 game season. (it has to be whole numbers as we are talking about games)
These numbers, modified by each of the answers, has to equal 0.58

a. 10
We can see that the smallest number of wins for 55% is 11. Eliminate

b. 14
11/20 becomes 14/23 = 0.6.... Too high. 22/40 is too many. Eliminate

c. 42
33/60 becomes 42/69 = 0.6..too much. So all of the others that have played less games than that would be too much too.
and all the other numbers are too high. Eliminate

d. 77
77/140 = 0.55
66/120 becomes 77/131=0.587...Pretty good
Anything smaller would be too much.
Keep D as it's pretty close, see if E gives an exact number

e. 87
77/140 becomes 87/150=0.58
Perfect
E

-----------

I initially tried solving it algebraically with
0.03=\(\frac{w+x}{w+l+x}\) - \(\frac{w}{w+l}\) but it didn't make things easy so had to go with the above.
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A baseball team’s season consists of playing 162 games.  [#permalink]

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New post 28 Oct 2018, 12:26
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harish1986 wrote:
A baseball team’s season consists of playing 162 games. At a certain point in its season, the team has won 55 percent of the games it has played. The team then wins a certain number of consecutive games so that at the end of the winning streak, the team has won 58 percent of the games it has played. How many wins did the team have at the end of its winning streak?

a. 10
b. 14
c. 42
d. 77
e. 87


let w=games won
p=games played
w=.58p→
w=29p/50→
w/29=p/50
only 87, a multiple of 29, will make w an integer
E
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Re: A baseball team’s season consists of playing 162 games.  [#permalink]

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New post 29 Oct 2018, 18:37
Bunuel, has there been analysis of what makes some quant questions particularly difficult?
gracie shows that this question can be very simple and not abstract, yet, at the time of writing answer distribution is
A 24%
B 18%
C 18%
D 24%
E 18%
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Re: A baseball team’s season consists of playing 162 games.  [#permalink]

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New post 30 Oct 2018, 19:06
2
harish1986 wrote:
A baseball team’s season consists of playing 162 games. At a certain point in its season, the team has won 55 percent of the games it has played. The team then wins a certain number of consecutive games so that at the end of the winning streak, the team has won 58 percent of the games it has played. How many wins did the team have at the end of its winning streak?

a. 10
b. 14
c. 42
d. 77
e. 87


We can let n = the number of games they have played right before the winning streak and w = the number games they have won during the winning streak. We can create the following equation:

(0.55n + w)/(n + w) = 0.58

0.55n + w = 0.58n + 0.58w

0.42w = 0.03n

42w = 3n

14w = n

From the above, we see that n is a multiple of 14. Furthermore, since 0.55n = 11/20 x n = 11n/20 is a whole number, we see that n is a multiple of 20. A multiple of 20 that is also a multiple of 14 is their LCM, which is 140 (the next common multiple is 280, but that is greater than 182 already). Therefore, n must be 140 and w must be 10. So the number of games they have won at the end of their winning streak is 0.55 x 140 + 10 = 77 + 10 = 87.

Alternate Solution:

We know that the number of games played and the number of games won at the end of the winning streak both need to be whole numbers. If we let n be the total number of games played at the end of the winning streak, then 0.58n, or 58n/100 = 29n/50 must be a whole number. Notice that 29 and 50 have no common factors and 29n/50 is the number of games won at the end of the winning streak; therefore, the number of games won at the end of the winning streak must be a multiple of 29. Among the choices, only 87 = 29 x 3 is a multiple of 29; therefore, it is the correct answer.

Answer: E
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Re: A baseball team’s season consists of playing 162 games.   [#permalink] 30 Oct 2018, 19:06
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