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10 Feb 2022, 09:40
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A
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Difficulty:
45%
(medium)
Question Stats:
63% (01:49) correct
37%
(02:00)
wrong
based on 167
sessions
History
Date
Time
Result
Not Attempted Yet
Find the value of N which satisfies the equation
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
10 Feb 2022, 22:04
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gmatcafe
Find the value of N which satisfies the equation
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
\(\frac{1+2+....+N}{100}=100*N\)
\(1+2+3+......N=100*100N\)
\(\frac{N(N+1)}{2}=10000N\)
\(N(N+1)=20000N\)
Since N is positive, we can divide both sides by N.
\(N+1=20000\)
\(N=19999\)
A
11 Feb 2022, 00:12
Kudos
Bookmarks
gmatcafe
Find the value of N which satisfies the equation
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
\(\frac{1}{100}\) + \(\frac{2}{100}\) + ... + \(\frac{N}{100}\) = 100 * N
A. 19999
B. 9999
C. 21999
D. 999
E. 1999
N*(N+1) /2 = 100*100*N
=> N(N-19999) =0
Therefore IMO A
