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05 Aug 2024, 19:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
48% (02:29) correct
52%
(02:29)
wrong
based on 86
sessions
History
Date
Time
Result
Not Attempted Yet
On day one, there are 100 particles in a laboratory experiment. On day n, where n >= 2 , one out of every n particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals
A. 16
B. 17
C. 18
D. 19
E. 20
A. 16
B. 17
C. 18
D. 19
E. 20
09 Sep 2024, 10:40
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\(a_1\): 100 particles
Day n (where n≥2): One out of every n particles produces another particle.
\(a_2\) : 100 + (1/2)*100 = 100 + 50 = 150
\(a_3\) : 150 + (1/3)*150 = 150 + 50 = 200
a_4 : 200 + (1/4)*200 = 200 + 50 = 250
and so on..
We need to find \(a_m\) such that \(a_m\) = 1000
Notice how every subsequent term is 50 more than the previous term => We have an AP (where \(a_1\) = 100, d = 50)
\(a_m\) = \(a_1\) + (m-1)*d = 1000
\(a_m\) = 100 + (m-1)*50 = 1000
(m-1)*50 = 900
m-1 = (900/50) => 18
Therefore, m = 19.
Day n (where n≥2): One out of every n particles produces another particle.
\(a_2\) : 100 + (1/2)*100 = 100 + 50 = 150
\(a_3\) : 150 + (1/3)*150 = 150 + 50 = 200
a_4 : 200 + (1/4)*200 = 200 + 50 = 250
and so on..
We need to find \(a_m\) such that \(a_m\) = 1000
Notice how every subsequent term is 50 more than the previous term => We have an AP (where \(a_1\) = 100, d = 50)
\(a_m\) = \(a_1\) + (m-1)*d = 1000
\(a_m\) = 100 + (m-1)*50 = 1000
(m-1)*50 = 900
m-1 = (900/50) => 18
Therefore, m = 19.
11 Sep 2024, 08:07
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I solved as expected and got D...However a minor grammatical correction in the question that will clarify a gret deal of things - "If the total number of particles in the laboratory experiment increases t̶o̶ by 1000 on day m, then m equals
