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Tips on remembering Reciprocals of first few digits  [#permalink]

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Hello!

I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google! I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/

Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.

Reciprocal of 2

Simplest of the Lot. Reciprocal of $$2 = \frac{1}{2} = 0.5 = 50$$%

Reciprocal of 3

Reciprocal of $$3 = \frac{1}{3} = 0.3333 = 33.33$$%. Reciprocal of 3 contains all 3's.

Reciprocal of 4

Remember 4 parts of a 25 makes a hundred. So, Reciprocal of $$4 = \frac{1}{4} = 0.25 = 25$$%

Reciprocal of 5

If $$\frac{1}{2}$$ is 0.5 then $$\frac{1}{5}$$ is 0.2 = 20%! Obviously!

Reciprocal of 6

Reciprocal of $$6 = \frac{1}{6} = 0.1666 = 16.66$$%. You can memorize this or, you can half the reciprocal of 3.

Reciprocal of 7 and its multiples

Remember this sequence - 1 4 2 8 5 7

Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.

$$\frac{1}{7} = 0.142857 = 14.2857$$% --> starts with the smallest number (1) in the sequence.

$$\frac{2}{7} = 0.285714 = 28.5714$$% --> same cycle but starts with the second smallest number (2) in the sequence

$$\frac{3}{7} = 0.428571 = 48.8571$$% --> same cycle but starts with the third smallest number (4) in the sequence

$$\frac{4}{7} = 0.571428 = 57.1428$$% --> same cycle but starts with the fourth smallest number (5) in the sequence

$$\frac{5}{7} = 0.714285 = 71.4285$$% --> same cycle but starts with the fifth smallest number (7) in the sequence

$$\frac{6}{7} = 0.857142 = 85.7142$$% --> same cycle but starts with the sixth smallest number (8) in the sequence

Reciprocal of 8 and its multiples

$$\frac{1}{8} = 0.125 = 12.5$$% --> Remember this as half of $$\frac{1}{4}$$. From this you can easily derive all other multiples

$$\frac{2}{8} = \frac{1}{4} = 0.25 = 25$$%

$$\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5$$%

$$\frac{4}{8} = \frac{1}{2}= 0.5 = 50$$%

$$\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5$$%

$$\frac{6}{8} = \frac{3}{4} = 0.75 = 75$$%

$$\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5$$%

Reciprocal of 9 and its multiples

$$\frac{1}{9} = 0.1111 = 11.11%$$

$$\frac{2}{9} = 0.2222 = 22.22%$$

....
....

$$\frac{8}{9} = 0.8888 = 88.88%$$

I bet you will never forget it now!

Reciprocal of 10

Another easy one = 0.1

Reciprocal of 11

$$\frac{1}{11} = 0.0909090$$... (Just something to help you recall : 1/9 has all 1's. 1/11 will have alternating 9)

Post this all the multiples will be multiples of 9 for example

$$\frac{2}{11} = 0.1818181$$... ----> 9*2 = 18

$$\frac{3}{11} = 0.272727$$... ----> 9*3 = 27

$$\frac{4}{11} = 0.363636$$... ----> 9*4 = 36

.... and so on

Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.

Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!

Other helpful resources on same topic

_________________
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Originally posted by susheelh on 08 Jun 2017, 22:20.
Last edited by susheelh on 11 Jun 2017, 05:23, edited 4 times in total.
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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1
susheelh wrote:
Hello!

I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google! I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/

Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.

Reciprocal of 2

Simplest of the Lot. Reciprocal of $$2 = \frac{1}{2} = 0.5 = 50$$%

Reciprocal of 3

Reciprocal of $$3 = \frac{1}{3} = 0.3333 = 33.33$$%. Reciprocal of 3 contains all 3's.

Reciprocal of 4

Remember 4 parts of a 25 makes a hundred. So, Reciprocal of $$4 = \frac{1}{4} = 0.25 = 25$$%

Reciprocal of 5

If $$\frac{1}{2}$$ is 0.5 then $$\frac{1}{5}$$ is 0.2 = 20%! Obviously!

Reciprocal of 6

Reciprocal of $$6 = \frac{1}{6} = 0.1666 = 16.66$$%. You can memorize this or, you can half the reciprocal of 3.

Reciprocal of 7 and its multiples

Remember this sequence - 1 4 2 8 5 7

Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.

$$\frac{1}{7} = 0.142857 = 14.2857$$% --> starts with the smallest number (1) in the sequence.

$$\frac{2}{7} = 0.285714 = 28.5714$$% --> same cycle but starts with the second smallest number (2) in the sequence

$$\frac{3}{7} = 0.428571 = 48.8571$$% --> same cycle but starts with the third smallest number (4) in the sequence

$$\frac{4}{7} = 0.571428 = 57.1428$$% --> same cycle but starts with the fourth smallest number (5) in the sequence

$$\frac{5}{7} = 0.714285 = 71.4285$$% --> same cycle but starts with the fifth smallest number (7) in the sequence

$$\frac{6}{7} = 0.857142 = 85.7142$$% --> same cycle but starts with the sixth smallest number (8) in the sequence

Reciprocal of 8 and its multiples

$$\frac{1}{8} = 0.125 = 12.5$$% --> Remember this as half of $$\frac{1}{4}$$. From this you can easily derive all other multiples

$$\frac{2}{8} = \frac{1}{4} = 0.25 = 25$$%

$$\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5$$%

$$\frac{4}{8} = \frac{1}{2}= 0.5 = 50$$%

$$\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5$$%

$$\frac{6}{8} = \frac{3}{4} = 0.75 = 75$$%

$$\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5$$%

Reciprocal of 9 and its multiples

$$\frac{1}{9} = 0.1111 = 11.11%$$

$$\frac{2}{9} = 0.2222 = 22.22%$$

....
....

$$\frac{8}{9} = 0.8888 = 88.88%$$

I bet you will never forget it now!

Reciprocal of 10

Another easy one = 0.1

Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.

Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!

Great post!

Thank you!
Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)
Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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1
Thanks naorba for the letting me know this is helpful! One Kudos to you for the appreciation! naorba wrote:
susheelh wrote:
Hello!

I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google! I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/

Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.

Reciprocal of 2

Simplest of the Lot. Reciprocal of $$2 = \frac{1}{2} = 0.5 = 50$$%

Reciprocal of 3

Reciprocal of $$3 = \frac{1}{3} = 0.3333 = 33.33$$%. Reciprocal of 3 contains all 3's.

Reciprocal of 4

Remember 4 parts of a 25 makes a hundred. So, Reciprocal of $$4 = \frac{1}{4} = 0.25 = 25$$%

Reciprocal of 5

If $$\frac{1}{2}$$ is 0.5 then $$\frac{1}{5}$$ is 0.2 = 20%! Obviously!

Reciprocal of 6

Reciprocal of $$6 = \frac{1}{6} = 0.1666 = 16.66$$%. You can memorize this or, you can half the reciprocal of 3.

Reciprocal of 7 and its multiples

Remember this sequence - 1 4 2 8 5 7

Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.

$$\frac{1}{7} = 0.142857 = 14.2857$$% --> starts with the smallest number (1) in the sequence.

$$\frac{2}{7} = 0.285714 = 28.5714$$% --> same cycle but starts with the second smallest number (2) in the sequence

$$\frac{3}{7} = 0.428571 = 48.8571$$% --> same cycle but starts with the third smallest number (4) in the sequence

$$\frac{4}{7} = 0.571428 = 57.1428$$% --> same cycle but starts with the fourth smallest number (5) in the sequence

$$\frac{5}{7} = 0.714285 = 71.4285$$% --> same cycle but starts with the fifth smallest number (7) in the sequence

$$\frac{6}{7} = 0.857142 = 85.7142$$% --> same cycle but starts with the sixth smallest number (8) in the sequence

Reciprocal of 8 and its multiples

$$\frac{1}{8} = 0.125 = 12.5$$% --> Remember this as half of $$\frac{1}{4}$$. From this you can easily derive all other multiples

$$\frac{2}{8} = \frac{1}{4} = 0.25 = 25$$%

$$\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5$$%

$$\frac{4}{8} = \frac{1}{2}= 0.5 = 50$$%

$$\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5$$%

$$\frac{6}{8} = \frac{3}{4} = 0.75 = 75$$%

$$\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5$$%

Reciprocal of 9 and its multiples

$$\frac{1}{9} = 0.1111 = 11.11%$$

$$\frac{2}{9} = 0.2222 = 22.22%$$

....
....

$$\frac{8}{9} = 0.8888 = 88.88%$$

I bet you will never forget it now!

Reciprocal of 10

Another easy one = 0.1

Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.

Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!

Great post!

Thank you!

_________________
My Best is yet to come!
Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)
Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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Thanks naorba for the letting me know this is helpful! One Kudos to you for the appreciation! naorba wrote:
susheelh wrote:
Hello!

I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google! I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/

Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.

Reciprocal of 2

Simplest of the Lot. Reciprocal of $$2 = \frac{1}{2} = 0.5 = 50$$%

Reciprocal of 3

Reciprocal of $$3 = \frac{1}{3} = 0.3333 = 33.33$$%. Reciprocal of 3 contains all 3's.

Reciprocal of 4

Remember 4 parts of a 25 makes a hundred. So, Reciprocal of $$4 = \frac{1}{4} = 0.25 = 25$$%

Reciprocal of 5

If $$\frac{1}{2}$$ is 0.5 then $$\frac{1}{5}$$ is 0.2 = 20%! Obviously!

Reciprocal of 6

Reciprocal of $$6 = \frac{1}{6} = 0.1666 = 16.66$$%. You can memorize this or, you can half the reciprocal of 3.

Reciprocal of 7 and its multiples

Remember this sequence - 1 4 2 8 5 7

Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.

$$\frac{1}{7} = 0.142857 = 14.2857$$% --> starts with the smallest number (1) in the sequence.

$$\frac{2}{7} = 0.285714 = 28.5714$$% --> same cycle but starts with the second smallest number (2) in the sequence

$$\frac{3}{7} = 0.428571 = 48.8571$$% --> same cycle but starts with the third smallest number (4) in the sequence

$$\frac{4}{7} = 0.571428 = 57.1428$$% --> same cycle but starts with the fourth smallest number (5) in the sequence

$$\frac{5}{7} = 0.714285 = 71.4285$$% --> same cycle but starts with the fifth smallest number (7) in the sequence

$$\frac{6}{7} = 0.857142 = 85.7142$$% --> same cycle but starts with the sixth smallest number (8) in the sequence

Reciprocal of 8 and its multiples

$$\frac{1}{8} = 0.125 = 12.5$$% --> Remember this as half of $$\frac{1}{4}$$. From this you can easily derive all other multiples

$$\frac{2}{8} = \frac{1}{4} = 0.25 = 25$$%

$$\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5$$%

$$\frac{4}{8} = \frac{1}{2}= 0.5 = 50$$%

$$\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5$$%

$$\frac{6}{8} = \frac{3}{4} = 0.75 = 75$$%

$$\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5$$%

Reciprocal of 9 and its multiples

$$\frac{1}{9} = 0.1111 = 11.11%$$

$$\frac{2}{9} = 0.2222 = 22.22%$$

....
....

$$\frac{8}{9} = 0.8888 = 88.88%$$

I bet you will never forget it now!

Reciprocal of 10

Another easy one = 0.1

Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.

Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!

Great post!

Thank you!

_________________
My Best is yet to come!
Intern  S
Joined: 06 May 2014
Posts: 44
Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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great tips!

wil surely try this. _________________
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.... Looking for some kudos here...
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GMAT 1: 720 Q48 V40 Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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Interesting info regarding fractions with base 7.

I use a neat trick to give me approximate value whenever I have fractions with base 7:

1. multiply the numerator of the fraction by 2
2. multiply number from step 1 by 7 and
3. place the number from step 2 after a decimal to get the approx value of the fraction

For example:
$$\frac{1}{7}$$ $$\approx{0.14}$$
From step 1, multiply numerator by 2 to get 2
From step 2, multiply 2 by 7 to get 14
From step 3, simply place a decimal to get the value as approx. 0.14

$$\frac{2}{7}$$ $$\approx{0.28}$$
From step 1, multiply numerator by 2 to get 4.
From step 2, multiply 4 by 7 to get 28
From step 3, simply place a decimal to get the value as approx. 0.28

similarly you can get
$$\frac{3}{7}$$ $$\approx{0.42}$$
$$\frac{4}{7}$$ $$\approx{0.56}$$
$$\frac{5}{7}$$ $$\approx{0.7}$$
$$\frac{2}{7}$$ $$\approx{0.84}$$

Note, all these are only approximate, so the result will be slightly smaller than actual value, but should be good enough for rough calculations.
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Joined: 12 Jun 2016
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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Thanks danlew!

This is definately something worth remembering. I am sure the text highlighted below is a typo and had to read - $$\frac{6}{7}$$ $$\approx{0.84}$$.

Also, very nicely explained danlew wrote:
Interesting info regarding fractions with base 7.

I use a neat trick to give me approximate value whenever I have fractions with base 7:

1. multiply the numerator of the fraction by 2
2. multiply number from step 1 by 7 and
3. place the number from step 2 after a decimal to get the approx value of the fraction

For example:
$$\frac{1}{7}$$ $$\approx{0.14}$$
From step 1, multiply numerator by 2 to get 2
From step 2, multiply 2 by 7 to get 14
From step 3, simply place a decimal to get the value as approx. 0.14

$$\frac{2}{7}$$ $$\approx{0.28}$$
From step 1, multiply numerator by 2 to get 4.
From step 2, multiply 4 by 7 to get 28
From step 3, simply place a decimal to get the value as approx. 0.28

similarly you can get
$$\frac{3}{7}$$ $$\approx{0.42}$$
$$\frac{4}{7}$$ $$\approx{0.56}$$
$$\frac{5}{7}$$ $$\approx{0.7}$$
$$\frac{2}{7}$$ $$\approx{0.84}$$

Note, all these are only approximate, so the result will be slightly smaller than actual value, but should be good enough for rough calculations.

_________________
My Best is yet to come!
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Joined: 18 Jun 2016
Posts: 257
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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danlew wrote:
Interesting info regarding fractions with base 7.

I use a neat trick to give me approximate value whenever I have fractions with base 7:

1. multiply the numerator of the fraction by 2
2. multiply number from step 1 by 7 and
3. place the number from step 2 after a decimal to get the approx value of the fraction

For example:
$$\frac{1}{7}$$ $$\approx{0.14}$$
From step 1, multiply numerator by 2 to get 2
From step 2, multiply 2 by 7 to get 14
From step 3, simply place a decimal to get the value as approx. 0.14

$$\frac{2}{7}$$ $$\approx{0.28}$$
From step 1, multiply numerator by 2 to get 4.
From step 2, multiply 4 by 7 to get 28
From step 3, simply place a decimal to get the value as approx. 0.28

similarly you can get
$$\frac{3}{7}$$ $$\approx{0.42}$$
$$\frac{4}{7}$$ $$\approx{0.56}$$
$$\frac{5}{7}$$ $$\approx{0.7}$$
$$\frac{2}{7}$$ $$\approx{0.84}$$

Note, all these are only approximate, so the result will be slightly smaller than actual value, but should be good enough for rough calculations.

Neat Trick. Thank you. Kudos Given.

Here is why this would work..
Let us assume that this is correct. Then,

$$\frac{x}{7}$$ ~ $$\frac{(x * 2 * 7)}{100}$$

=> x ~$$\frac{(x * 2 * 7 * 7)}{100}$$

2 * 7 * 7 = 98

Therefore,
x ~ $$\frac{(x * 98)}{100}$$
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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Great post yar. Thanks. Really it made life simpler.
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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hotcool030 wrote:
Great post yar. Thanks. Really it made life simpler.

There is another one missing from OP..

$$\frac{1}{11} = 0.09090..$$

Therefore, $$\frac{2}{11} = 0.1818..$$

$$\frac{3}{11} = 0.2727..$$

$$\frac{4}{11} = 0.3636..$$

And so on.
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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Hello umg,

Thanks for bringing this up. I have edited the main post to include this. Also, changed the name of the thread to - Tips on remembering Reciprocals of firs few digits umg wrote:
hotcool030 wrote:
Great post yar. Thanks. Really it made life simpler.

There is another one missing from OP..

$$\frac{1}{11} = 0.09090..$$

Therefore, $$\frac{2}{11} = 0.1818..$$

$$\frac{3}{11} = 0.2727..$$

$$\frac{4}{11} = 0.3636..$$

And so on.

_________________
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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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HI hotcool030,

Good to know that you found it useful! I myself am struggling with FDP problems - so, I can understand hotcool030 wrote:
Great post yar. Thanks. Really it made life simpler.

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Re: Tips on remembering Reciprocals of first few digits  [#permalink]

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_________________ Re: Tips on remembering Reciprocals of first few digits   [#permalink] 24 Feb 2019, 11:37
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