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04 Jan 2021, 23:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:54) correct
24%
(02:43)
wrong
based on 142
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If S is the product of integers from 100 to 300 inclusive, and if T is the product of integers 100 to 301, inclusive, what is \(\frac{1}{S} + \frac{1}{T}\) in terms of T?
A. \(\frac{3012}{T}\)
B. \(\frac{(302T)}{301}\)
C. \(302T\)
D. \(\frac{302}{T}\)
E. \((302)(301)T^2\)
A. \(\frac{3012}{T}\)
B. \(\frac{(302T)}{301}\)
C. \(302T\)
D. \(\frac{302}{T}\)
E. \((302)(301)T^2\)
05 Jan 2021, 10:33
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S=100*101.....300
T=100*101.....301
\(\frac{1}{S}+\frac{1}{T}=\frac{1}{100*101.....300}+\frac{1}{100*101.....301}\)
\(=\frac{1}{100*101.....300}(1+\frac{1}{301})\)
\(=\frac{1}{100*101.....300}(\frac{302}{301})\)
\(=\frac{302}{T}\)
IMO D
T=100*101.....301
\(\frac{1}{S}+\frac{1}{T}=\frac{1}{100*101.....300}+\frac{1}{100*101.....301}\)
\(=\frac{1}{100*101.....300}(1+\frac{1}{301})\)
\(=\frac{1}{100*101.....300}(\frac{302}{301})\)
\(=\frac{302}{T}\)
IMO D
05 Jan 2021, 10:47
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IMO D
T = 301 * s
1 / S = 301 / T
So 1 / T + 1/S = 301/T + 1/T
Which becomes 302/T
Posted from my mobile device
T = 301 * s
1 / S = 301 / T
So 1 / T + 1/S = 301/T + 1/T
Which becomes 302/T
Posted from my mobile device
