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1 + 1/(1 + 1/(1 + 1/3))

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GMATD11
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1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   13 Feb 2011, 06:45
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\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=\)


A. 4/7

B. 4/3

C. 11/8

D. 11/7

E. 7/4

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fraction.JPG
fraction.JPG [ 28.33 KiB | Viewed 12108 times ]
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1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   13 Feb 2011, 07:06
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\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=\)


A. 4/7

B. 4/3

C. 11/8

D. 11/7

E. 7/4


\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}\).

Answer: D.
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   24 Feb 2018, 12:24
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Bunuel wrote:
\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}\).

Answer: D.



Hi Bunuel, why did you move up one number "1" from denominator

the denominator looks like this as it is in the picture --> 1+1+\(\frac{1}{1+3}\) and denominator should equal 11/4

I got final answer 4/11 :?
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   24 Feb 2018, 14:48
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Aside: Bunuel is using a very useful (and often tested) fraction property that says: 1/(a/b) = b/a

Some examples:
1/(2/3) = 3/2
1/(8/5) = 5/8

MORE USEFUL FRACTION PROPERTIES HERE:
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   25 Feb 2018, 19:08
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dave13 wrote:
Bunuel wrote:
\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}\).

Answer: D.



Hi Bunuel, why did you move up one number "1" from denominator

the denominator looks like this as it is in the picture --> 1+1+\(\frac{1}{1+3}\) and denominator should equal 11/4

I got final answer 4/11 :?


dave13 He didn't move any denominator!!! He just simplified the denominator.

1+\(\frac{1}{3}\) = 4/3 & 1/(4/3)=3/4
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   28 Feb 2018, 11:25
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GMATD11 wrote:
Attachment:
fraction.JPG


Let’s first simplify 1 + 1/3:

1 + 1/3 = 4/3

1/(4/3) = 3/4. So we now have:

1 + 1/(1 + 3/4)

1 + 1/(7/4)

1 + 4/7 = 7/7 + 4/7 = 11/7

Answer: D
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   18 Aug 2018, 22:38
Bunuel wrote:
\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}\).

Answer: D.


Hi Bunuel,

Can you edit this question. The way it is shown in image is

1 / {1+1+ [1 / (1+1/3) ] }

And Also i tried to post it mathematically . But it wouldn't show up in the format .

\(\frac{1}{1+1 + [m][fraction]1/1+[fraction]1/3}[/fraction]\)[/fraction][/m]

Where am i going wrong
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   18 Aug 2018, 23:00
GMATD11 wrote:
Attachment:
fraction.JPG


Hi GMAT D11,

The question should be formatted like this to get OA as D.

1 + \(\frac{1}{1+\frac{1}{1+\frac{1}{3}}}\)

If we frame it like the image in the question answer seems to round upto -

\(\frac{4}{11}\)
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   19 Aug 2018, 08:35
adstudy wrote:
GMATD11 wrote:
Attachment:
fraction.JPG


Hi GMAT D11,

The question should be formatted like this to get OA as D.

1 + \(\frac{1}{1+\frac{1}{1+\frac{1}{3}}}\)

If we frame it like the image in the question answer seems to round upto -

\(\frac{4}{11}\)


:thumbup:
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1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   16 Sep 2019, 07:55
GMATD11 wrote:
\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=\)


A. 4/7

B. 4/3

C. 11/8

D. 11/7

E. 7/4

Show Spoiler
Attachment:
fraction.JPG



\(1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{3}{4}} = 1+\frac{4}{7} = \frac{11}{7}\)

IMO D
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Re: 1 + 1/(1 + 1/(1 + 1/3)) [#permalink] New post   28 Jun 2022, 00:02
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