If N = 1/3 + 1/3^2 +1/3^3 , then N is between

Hi All,

In certain Quant questions, the answer choices are designed to provide a significant 'shortcut' (so that you can avoid some of the 'math' involved if you recognize the pattern/concept that the question is built around).

Here, we're asked to think about the sum of 1/3 + 1/3^2 +1/3^3, but we're not actually asked to calculate it. The prompt asks for the RANGE that this total would fall into.

Since we're adding up 1/3 + 1/9 + 1/27, we can see that each fraction becomes significantly SMALLER than the one before it. If we were adding 1/3 + 1/3 + 1/3, then we'd have a total of 1. Here, the second two fractions are MUCH SMALLER than 1/3, so the total has to be FAR LESS than 1 (but greater than 1/3). There's only one answer that matches this deduction.

Final Answer:

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

I did by inference
if we add [1/9 = .11] to [1/3=.33] .. it gives .44
now we add [1/27~ 1/25 = .04] to .44 it gives .48 ~.5
now it does not drift 1/3 much from its position and it should stay close to 1/3
hence only one possible answer C

Hi tryambaks,

The ability to convert Quant data/information from one 'format' to another will be quite helpful on a handful of questions on Test Day, so you should continue to look for opportunities to use those skills as you practice.

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

there are two methods of doing this each method can take upto 50 Secs

First Method
1/3= 33.33%
1/9= 11.11%
1/27 will be 1/9( 33.33%) 3.70 %

addding we get it will be nearly equal to 49 % so the answer will be what

Each choice can be read as

A 0 and 1/9 can be read as 0% to 11% ( No)
B.1/9 and 1/3 can be read as 11% to 33% ( No)
C.1/3 and 8/9 can be read as 33% to 88% ( Ok seems in our range)
D.8/9 and 4/3 can be read as 88% to 133% ( No)
E. 4/3 and 2 can be read as 133% to 200% ( No)


Second method
if we can see the series is as GP then sum is given by
a{1-(r)^n}/{1-r}

a= 1/3 , r=1/3

Now 1/3{1-1/27}/{1-1/3}
={26/27*3}2/3
= 13/27

ok so 13/26 = 1/2=.5 and 13/26>13/27 so thus value is slightly less than .5
So only option C it says between .333 to .8888

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

No need to even do any addition i think for this question...

1/3 is >> 1/9
1/3 is >>>1/27

So essentially we are adding 2 very small quantities to 1/3.This addition therefore wont exceed 1/3 by a large amount.Therefore C

Posted from my mobile device

Sum of infinite GP is
a/1-a
(1/3)/{1-(1/3)}=1/2
Clearly C is answer

Posted from my mobile device

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

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