A cricketer made 90 runs in his 12th inning, and his average declined by 5 runs. Find his new average after the 12th innings.
a)127
b)145
c)150
d)180
e)217
OA : [spoiler]B[/spoiler]
I got the answer but I need short cuts please
An average problem
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 GMATGuruNY
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We can PLUG IN THE ANSWERS, which represent the average after 12 innings.coolhabhi wrote:A cricketer made 90 runs in his 12th inning, and his average declined by 5 runs. Find his new average after the 12th innings.
a)127
b)145
c)150
d)180
e)217
Since the average after the 12th inning decreases by 5 runs, the answer choices imply the following options for the average after 11 innings:
127 + 5 = 132.
145 + 5 = 150.
150 + 5 = 155.
180 + 5 = 185.
217 + 5 = 222.
Given that the number of runs made in the 12th inning is a MULTIPLE OF 10, the most likely answer choice is B  the only option that yields a multiple of 10 for the average after 11 innings.
When the correct answer choice is plugged in, 90 runs will be made in the 12th inning.
Answer choice B:
Total runs after 12 innings = (number of innings)(average per inning) = 12*145 = 1740.
Total runs after 11 innings = (number of innings)(average per inning) = 11*150 = 1650.
Runs made in the 12th inning = (total for all 12 innings)  (total for the first 11 innings) = 17401650 = 90.
Success!
The correct answer is B.
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 Brent@GMATPrepNow
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Let F = TOTAL # of runs for the first 11 inningscoolhabhi wrote:A cricketer made 90 runs in his 12th inning, and his average declined by 5 runs. Find his new average after the 12th innings.
a)127
b)145
c)150
d)180
e)217
So, F + 90 = TOTAL # of runs for 12 innings
Let A = Average runs per inning after 12 innings [note: our goal is to find the value of A]
So A + 5 = Average runs per inning after 11 innings [since we're told that, his average was 5 runs MORE after 11 innings]
So, F/11 = A + 5 [total number of runs for 11 innings/11 innings = average runs per inning]
Also, (F + 90)/12 = A [total number of runs for 12 innings/12 innings = new average runs per inning]
We now have two equations with 2 variables:
F/11 = A + 5
(F + 90)/12 = A
Take 1st equation and cross multiply to get: 11A + 55 = F
Take 2nd equation and cross multiply to get 12A = F + 90 . Rearrange to get: 12A  90 = F
Since BOTH equations are equal to F, we can conclude that 11A + 55 = 12A  90
Solve to get A = 145
Answer: B
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I think we can also do the following:
sum of first 11 rounds is 11M
so for the 12 rounds: (11M+90)/12 = M5
11M+90 = 12M60 Subtract 11M from both sides and add 60 to both sides
150 = M
Hence M5 = 1505 = 145
BINGO!
sum of first 11 rounds is 11M
so for the 12 rounds: (11M+90)/12 = M5
11M+90 = 12M60 Subtract 11M from both sides and add 60 to both sides
150 = M
Hence M5 = 1505 = 145
BINGO!
Brent@GMATPrepNow wrote:Let F = TOTAL # of runs for the first 11 inningscoolhabhi wrote:A cricketer made 90 runs in his 12th inning, and his average declined by 5 runs. Find his new average after the 12th innings.
a)127
b)145
c)150
d)180
e)217
So, F + 90 = TOTAL # of runs for 12 innings
Let A = Average runs per inning after 12 innings [note: our goal is to find the value of A]
So A + 5 = Average runs per inning after 11 innings [since we're told that, his average was 5 runs MORE after 11 innings]
So, F/11 = A + 5 [total number of runs for 11 innings/11 innings = average runs per inning]
Also, (F + 90)/12 = A [total number of runs for 12 innings/12 innings = new average runs per inning]
We now have two equations with 2 variables:
F/11 = A + 5
(F + 90)/12 = A
Take 1st equation and cross multiply to get: 11A + 55 = F
Take 2nd equation and cross multiply to get 12A = F + 90 . Rearrange to get: 12A  90 = F
Since BOTH equations are equal to F, we can conclude that 11A + 55 = 12A  90
Solve to get A = 145
Answer: B
Cheers,
Brent

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Suppose the average of the first 11 innings was x.
We know that
(Previous Run Total)/11 = x
and that
(Previous Run Total)/11 = 5 + ((Previous Run Total + 90)/12)
so we have
x = 5 + (11x + 90)/12
12x = 60 + 11x + 90
x = 150
Since x is our old average, our new average = 150  5 => 145
We know that
(Previous Run Total)/11 = x
and that
(Previous Run Total)/11 = 5 + ((Previous Run Total + 90)/12)
so we have
x = 5 + (11x + 90)/12
12x = 60 + 11x + 90
x = 150
Since x is our old average, our new average = 150  5 => 145