If \(N = \dfrac13 + \dfrac1{3^2} +\dfrac1{3^3},\) then \(N\) is between

[M7MBA]

If \(N = \dfrac13 + \dfrac1{3^2} +\dfrac1{3^3},\) then \(N\) is between

A. \(0\) and \(\dfrac19\)

B. \(\dfrac19\) and \(\dfrac13\)

C. \(\dfrac13\) and \(\dfrac89\)

D. \(\dfrac89\) and \(\dfrac43\)

E. \(\dfrac43\) and \(2\)

Answer: C

Source: GMAT Prep

[Brent@GMATPrepNow]

If \(N = \dfrac13 + \dfrac1{3^2} +\dfrac1{3^3},\) then \(N\) is between

A. \(0\) and \(\dfrac19\)

B. \(\dfrac19\) and \(\dfrac13\)

C. \(\dfrac13\) and \(\dfrac89\)

D. \(\dfrac89\) and \(\dfrac43\)

E. \(\dfrac43\) and \(2\)

Answer: C

Source: GMAT Prep

N = 1/3 + 1/3^2 +1/3^3
= 1/3 + 1/9 + 1/27
= 9/27 + 3/27 + 1/27
= 13/27

C) between 1/3 and 8/9 is the same as between 9/27 and 24/27
Since 13/27 is between 9/27 and 24/27, the correct answer is C