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

Question

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

chetan2u · Accepted Answer

hi,
the Q is simple and can be done with simple addition..

N = \frac{1}{3} + \frac{1}{3^2} +\frac{1}{3^3} =\frac{1}{3} + \frac{1}{9} +\frac{1}{27}= \frac{(9+3+1)}{27}=\frac{13}{27} , which is clearly close to 1/2 
and will fit in range of 1/3 and 8/9..

If a number is series or contains a large number of fractions we can work on estimate to get the answer..
  N = \frac{1}{3} + \frac{1}{3^2} +\frac{1}{3^3}

two values which can be easily seen are Min and Max ..
N>1/3 and N<1.. only C and D fit in..
Each term in N is 1/3 of the pervious term so cannot be closer to 1..
only C is left

EMPOWERgmatRichC · Answer

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:  C

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

NoHalfMeasures · Answer

chetan2u I know its an easy question. but I decided to go a little pedantic in case gmat asks a more challenging question of this type

It is a geometric progression with a=r= 1/3 sum=1/3* {1- (1/3)^n}/{1-(1/3)} = 13/27 ~ less than .50 Ans C

tryambaks · Answer

I did by inference
if we add   to   .. it gives .44
now we add   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

EMPOWERgmatRichC · Answer

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

AbhimanyuDhar · Answer

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

JeffTargetTestPrep · Answer

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

redskull1 · Answer

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

Mohitstarc · Answer

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

Posted from my mobile device

BrentGMATPrepNow · Answer

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

ManifestDreamMBA · Answer

N = 1/3 + 1/3^2 +1/3^3
N > 1/3
Eliminate A,B

If all the terms were 1/3, N would have been 1. However 1/3^2 and 1/3^3 are much smaller, so answer is less than 1
Eliminate E
1/3^2 +1/3^3
1/3^2 * (1+1/3)
1/3^2 *4/3
4/27 < 1/3

N = 1/3 + 1/3^2 +1/3^3 = 1/3 + 4/27 < 2/3
Eliminate D

Answer C

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

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

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