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Picnic

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by knight247 » Tue Jul 12, 2011 10:41 am
Every student of a certain class in a School volunteered to contribute equally for the a picnic. If the total contribution received was $600, how many students were there in the class?
(1)Each student contributed $10
(2)10 students failed to contribute and the remaining students ended up paying $2 more than they would have contributed otherwise.

OA is [spoiler](A)[/spoiler] but I disagree with the OA. In my opinion it is [spoiler](D)[/spoiler]

Lets hear everyone's opinion and then i'll explain my opinion.thanks
Last edited by knight247 on Tue Jul 12, 2011 12:42 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by clock60 » Tue Jul 12, 2011 11:18 am
agree with D, 2 st is also valid as it gives number of persons=60 and -50, but the number can`t -ve so must be neglected
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by Anurag@Gurome » Tue Jul 12, 2011 7:10 pm
knight247 wrote:Every student of a certain class in a School volunteered to contribute equally for the a picnic. If the total contribution received was $600, how many students were there in the class?
(1)Each student contributed $10
(2)10 students failed to contribute and the remaining students ended up paying $2 more than they would have contributed otherwise.
Say number of students in the class is n and each of them contributed $m for the picnic. Hence, mn = 600

Therefore, number of students in the class, n = 600/m

Statement 1: m = 10 --> n = 600/10 = 60

Sufficient

Statement 2: (n - 10)(m + 2) = 600 --> mn + 2n - 10m = 620
Replacing m = 600/n in the above equation,
  • --> (600/n)n + 2n - 10(600/n) - 620 = 0
    --> 600 + 2n - 6000/n - 620 = 0
    --> 2n - 20 - 6000/n = 0
    --> 2n² - 20n - 6000 = 0
    --> n² - 10n - 3000 = 0
    --> (n - 60)(n + 50) = 0
As n cannot be negative, only possible value of n is 60.

Sufficient

The correct answer is D.
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