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A certain school has 50 students assigned randomly to 5 dist

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A certain school has 50 students assigned randomly to 5 dist [#permalink]  14 Apr 2019, 10:54
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A certain school has 50 students assigned randomly to 5 distinct classes, and each student is assigned to only one class. If the quantities of students in the 5 classes are consecutive numbers, what is the probability that a given student is in one of the two largest classes?

A. 48%

B. 46%

C. 42%

D. 38%

E. 34%
[Reveal] Spoiler: OA

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Re: A certain school has 50 students assigned randomly to 5 dist [#permalink]  14 Apr 2019, 15:04
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Expert's post
Carcass wrote:
A certain school has 50 students assigned randomly to 5 distinct classes, and each student is assigned to only one class. If the quantities of students in the 5 classes are consecutive numbers, what is the probability that a given student is in one of the two largest classes?

A. 48%

B. 46%

C. 42%

D. 38%

E. 34%

The quantities of students in the 5 classes are consecutive numbers
Let x = number of students in smallest class
So, x+1 = number of students in next class
x+2 = number of students in middle-sized class
x+3 = number of students in second biggest class
x+4 = number of students in biggest class

We can write: x + x+1 + x+2 + x+3 + x+4 = 50
Simplify: 5x + 10 = 50
So 5x = 40
Solve: x = 40/5 = 8
So, there are 8 students in the smallest class
9 students in the next class
10 students in middle-sized class
11 students in second biggest class
12 students in biggest class

11 + 12 = 23

So, 23 of the 50 students are in the 2 largest classes.
So, P(given student is in one of the two largest classes?) = 23/50 = 0.46

Cheers,
Brent
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Re: A certain school has 50 students assigned randomly to 5 dist [#permalink]  22 Apr 2019, 13:52
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Number of people in 5 classes is consecutive, meaning there are a students in class 1, a+1 in class 2 and.... a+4 in class 5. So:
a + (a+1) + (a+2) + (a+3) + (a+4) = 50
5a + 10 = 50
a = 8
So the number of students in the classes are 8,9,10,11,12
The probability that a student be a one of the 11 or 12 students is (12+11)/ 50 = 23/50 = 46%
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Re: A certain school has 50 students assigned randomly to 5 dist   [#permalink] 22 Apr 2019, 13:52
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