GMAT Prep If n= 1/3

barksdale wrote:From GMAT Prep. If n= 1/3 +1/3^2+1/3^3 then N is between

A) 0 and 1/9
B) 1/9 and 1/3
C) 1/3 and 8/9
D) 8/9 and 4/3
E) 4/3 and 2

n= 1/3 + 1/3^2 + 1/3^3
= 1/3 + 1/9 + 1/27
= 9/27 + 3/27 + 1/27
= 13/27
≈ 1/2

Answer: C

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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Manhattan Review GMAT Prep

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Hi barksdale,

The answer choices to this question are all RANGES, so you're not necessarily going to have to calculate the exact value of that sum (you can probably just estimate it and get the correct answer).

To start, you should notice two things:
1) We're adding 3 fractions.
2) Raising a positive fraction to an exponent greater than 1 will make the fraction SMALLER.

If we were adding 1/3 + 1/3 + 1/3, then we'd have a sum of 1. However, while the first number is 1/3, we're adding two increasingly smaller fractions to it, so we're going to end up with a sum that is considerably smaller than 1... but still bigger than 1/3. There's only one answer that 'fits'...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Here's a similar question to practice with: https://www.beatthegmat.com/m-is-the-sum ... 94397.html

Cheers,
Brent

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

We can add together the given equation:

n = 1/3 + 1/3^2 + 1/3^3

n = 1/3 + 1/9 + 1/27

n = 9/27 + 3/27 + 1/27 = 13/27

We see that 13/27 is just under 1/2, thus n is between 1/3 and 8/9.

Answer: C