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A certain office building houses five departments of the same company

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A certain office building houses five departments of the same company [#permalink] New post   01 Oct 2021, 09:27
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A certain office building houses five departments of the same company and exactly 75 employees. If the numbers of employees working in the departments are consecutive odd numbers, what is the probability that a given employee works in one of the two largest departments?

(A) 48%
(B) 45%
(C) 44%
(D) 40%
(E) 32%
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A
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A certain office building houses five departments of the same company [#permalink] New post   01 Oct 2021, 19:29
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Total employee \(= 75\) in five department

Five Consecutive ODD integers: \(2x - 3, 2x - 1, 2x + 1, 2x + 3, 2x + 5\)

Sum \(= 75 = 10x + 5\)

\(x = 7\)

Numbers \(= 11 , 13 , 15 , 17 , 19\)

Probability of a given employee works in one of the two largest departments \(= \frac{ 19 + 17 }{ 75} = \frac{36}{75} = \) \(= 48\)%

Answer A
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A certain office building houses five departments of the same company [#permalink] New post   01 Oct 2021, 19:35
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I think your answer above is incorrect. it asks for 5 consecutive odd integers. So it would be.

Total employee =75=75 in five department

Five Consecutive odd integers: x,x+2,x+4,x,x+6,x+8 = 75

Solve for x
x=11


Numbers =11,13,15,17,19

Probability of a given employee works in one of the two largest departments =(17+19)/75 = 48% or A
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A certain office building houses five departments of the same company [#permalink] New post   01 Oct 2021, 19:40
1
Sir,

Thanks for pointing it out. I've edited it accordingly.

vchen wrote:
I think your answer above is incorrect. it asks for 5 consecutive odd integers. So it would be.

Total employee =75=75 in five department

Five Consecutive odd integers: x,x+2,x+4,x,x+6,x+8 = 75

Solve for x
x=11


Numbers =11,13,15,17,19

Probability of a given employee works in one of the two largest departments =(17+19)/75 = 48% or A
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A certain office building houses five departments of the same company [#permalink]
01 Oct 2021, 19:40
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