barksdale wrote:From GMAT Prep. If n= 1/3 +1/3^2+1/3^3 then N is between
0 and 1/9
1/9 and 1/3
1/3 and 8/9
8/9 and 4/3
4/3 and 2
What is our thought process to get through this math without a calculator or spreadsheet for that matter?
The most efficient way to solve this question is by finding the value of n in fractional form.
We have:
n = 1/3 +1/3^2+1/3^3
= 1/3 + 1/9 + 1/27
= (9+3+1)/27 = 13/27
Let's make the denominator of the options '27 ' and check that in which of the options '13/27' falls.
A. 0 and 1/9 => 0 and 3/27. Rejected as 13/27 > upper value 3/27.
B. 1/9 and 1/3 => 3/27 and 9/27. Rejected as 13/27 > upper value 9/27.
C. 1/3 and 8/9 => 9/27 and 24/27. Correct answer as 13/27 falls within 9/27 and 24/27.
D. 8/9 and 4/3 => 24/27 and 36/27. Rejected as 13/27 < lower value 24/27.
E. 4/3 and 2 => 36/27 and 54/27. Rejected as 13/27 < lower value 36/27.
The correct answer:
C
Hope this helps!
Relevant book:
Manhattan Review GMAT Math Essentials Guide
-Jay
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