GMAT Prep If n= 1/3

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barksdale: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue May 30, 2017 6:47 pm; Thanked: 1 times

by barksdale » Tue May 30, 2017 6:54 pm

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?

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Source: Beat The GMAT — Problem Solving | Tue May 30, 2017 6:54 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 30, 2017 7:00 pm

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
â‰ˆ 1/2

Answer: C

Brent Hanneson - Creator of GMATPrepNow.com

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue May 30, 2017 8:47 pm

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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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue May 30, 2017 9:48 pm

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

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Rich

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed May 31, 2017 4:22 am

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jun 01, 2017 4:08 pm

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

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Founder and CEO
[email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Jun 05, 2017 11:07 pm

In general, we could say that

x + xÂ² + xÂ³ =>

x * (1 + x + xÂ²) = >

x * (1 + x * (1 + x))

which makes funkier numbers a little easier to approximate.

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Balla: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Jul 28, 2017 7:21 pm

by Balla » Wed Aug 09, 2017 6:27 pm

1/3 +1/9 +1/27=x

1+1/3 +1/9=3x

2x=1-1/27=26/27

x=13/27

so by visualizing a number line it is clear choice c works

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