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If n is a positive integer, which of the following could be equal to
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09 Oct 2023, 21:32
09 Oct 2023, 21:32
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If n is a positive integer, which of the following could be equal to \(((n+1)^3) - ((n^3)+1)\)?
A. \(7^3(6^3-1)\)
B. \(7^3(6^3+1)\)
C. \(2*26*27\)
D. \(3*31*32\)
E. \(0\)
A. \(7^3(6^3-1)\)
B. \(7^3(6^3+1)\)
C. \(2*26*27\)
D. \(3*31*32\)
E. \(0\)
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3130
Given Kudos: 1857
Location: India
Concentration: Strategy, Leadership
Re: If n is a positive integer, which of the following could be equal to
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09 Oct 2023, 22:15
09 Oct 2023, 22:15
2
Kudos
nick13 wrote:
if n is a positive integer, which of the following could be equal to ((n+1)^3) - ((n^3)+1)?
A. (7^3) ((6^3)-1)
B.(7^3) ((6^3)+1)
C. 2*26*27
D. 3*31*32
E. 0
A. (7^3) ((6^3)-1)
B.(7^3) ((6^3)+1)
C. 2*26*27
D. 3*31*32
E. 0
\((n+1)^3 = n^3 + 1^3 + 3*n^2*1 + 3*1^2*n = n^3 + 1^3 + 3n^2 + 3n\)
Substituting the expanded form in the equation
\(n^3 + 1^3 + 3n^2 + 3n - (n^3 + 1) \)
\(n^3 + 1 + 3n^2 + 3n - n^3 - 1 \)
\(3n^2 + 3n\)
\(3n(n+1)\)
Option D matches with the above format for \(n = 31\)
Re: If n is a positive integer, which of the following could be equal to
[#permalink]
10 Oct 2023, 00:25
10 Oct 2023, 00:25
Asked: If n is a positive integer, which of the following could be equal to \(((n+1)^3) - ((n^3)+1)\)?
\(((n+1)^3) - ((n^3)+1) = (n+1)ˆ3 - nˆ3 - 1 = 3nˆ2 + 3n = 3n(n+1) \)
IMO D
\(((n+1)^3) - ((n^3)+1) = (n+1)ˆ3 - nˆ3 - 1 = 3nˆ2 + 3n = 3n(n+1) \)
IMO D
