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Manager  Joined: 10 Nov 2010
Posts: 175
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21 WE: Information Technology (Computer Software)
1 + 1/(1 + 1/(1 + 1/3))  [#permalink]

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1 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:14) correct 15% (01:45) wrong based on 199 sessions

### HideShow timer Statistics $$1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=$$

A. 4/7

B. 4/3

C. 11/8

D. 11/7

E. 7/4

Attachment: fraction.JPG [ 28.33 KiB | Viewed 3527 times ]

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Math Expert V
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Posts: 56371
1 + 1/(1 + 1/(1 + 1/3))  [#permalink]

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1
2
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=$$

A. 4/7

B. 4/3

C. 11/8

D. 11/7

E. 7/4

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

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Re: 1 + 1/(1 + 1/(1 + 1/3))  [#permalink]

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Bunuel wrote:
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}$$.

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 CEO  V
Joined: 12 Sep 2015
Posts: 3857
Re: 1 + 1/(1 + 1/(1 + 1/3))  [#permalink]

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Top Contributor
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]

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1
dave13 wrote:
Bunuel wrote:
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}$$.

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]

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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

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Re: 1 + 1/(1 + 1/(1 + 1/3))  [#permalink]

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Bunuel wrote:
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{3}}}=1+\frac{1}{1+\frac{1}{\frac{4}{3}}}=1+\frac{1}{1+\frac{3}{4}}=1+\frac{1}{\frac{7}{4}}=1+\frac{4}{7}=\frac{11}{7}$$.

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]

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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]

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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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"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas Re: 1 + 1/(1 + 1/(1 + 1/3))   [#permalink] 19 Aug 2018, 08:35
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