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# What is the 25th digit to the right of the decimal point in

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What is the 25th digit to the right of the decimal point in [#permalink]

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13 Aug 2012, 07:06
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What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Practice Questions
Question: 20
Page: 154
Difficulty: 600
[Reveal] Spoiler: OA

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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13 Aug 2012, 07:06
2
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Expert's post
SOLUTION

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

$$\frac{6}{11}=0.5454...$$.

Every odd-numbered digit, to the right of the decimal point, is 5, thus 25th (odd) digit will also be 5.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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13 Aug 2012, 07:52
6/11=0.54545454 repeating, with 5 occuring at 1,3,5,7 etc. So the 25th digit will be 5.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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16 Aug 2012, 11:48
1
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C) 5
Same solution as above, but in case the repeating digits are more numerous then see:
1) Number of repeating digits (in this case 2 -> .5454..)
2) Divide the # of the digit you're supposed to view (25th digit) by # of repeats = (25/2)th digit
3) If no remainder, then its 4, if there's a Remainder = 1 then it has to be the next digit or 5, as in this case
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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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16 Aug 2012, 12:35
2
KUDOS
6/11 results in a Non-terminating decimal equal to .545454......54
Every even place (2nd,4th,6th,,,,,,,,,24th) digit is 4.
Every Odd place (1,3,5.....25) digit is 5.
Thus thus the odd place digit is 5
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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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17 Aug 2012, 01:12
1
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Expert's post
SOLUTION

What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

$$\frac{6}{11}=0.5454...$$.

Every odd-numbered digit, to the right of the decimal point, is 5, thus 25th (odd) digit will also be 5.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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02 Aug 2013, 13:07
5
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an easy way to find 6/11 in decimal terms

expand it by 9

(6*9)/(11*9) = 54/99

note that 54/99 is the fractional representation of circulating (recurring) decimal 0,545454...

___

I dunno how anyone else would of got 0.5454 etc without using a calculator

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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03 Nov 2013, 13:13
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But is there anyway to remember how to calculate 6/11 or 7/11 for that matter?I can't possibly remember all fractions...

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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03 Nov 2013, 13:18
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Expert's post
Markster wrote:
But is there anyway to remember how to calculate 6/11 or 7/11 for that matter?I can't possibly remember all fractions...

Try to simply divide 6 by 11 to get 0.5454...

Else notice that 6/11=54/99=0.5454... Check Converting Decimals to Fractions here: math-number-theory-88376.html
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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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09 Sep 2014, 23:57
2
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Bunuel wrote:
What is the 25th digit to the right of the decimal point in the decimal form of 6/11?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Practice Questions
Question: 20
Page: 154
Difficulty: 600

multiply 9 on both 6 & 11 then u will get 54/99...

whatever 2 digit number divided 99 will have the same digits repeat... say here 0.5454....

25th digit will be 5....

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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29 Apr 2015, 06:29
Just want to be clear here. Are we expected to know non terminating fractions or expected to do the math of 6/11? I could do, but I felt it would be math intensive and wanted to avoid that. The rule that seemed relevant from the number theory link is that terminating fractions have a denominator that fits the 2^m*5^n formula. What's the best way to approach this, and what math is unnecessary? Please advise.

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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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29 Apr 2015, 09:37
I divided 6/11 and got to .545, after that I realized the pattern would repeat itself. As there's just two different digits the even decimals will be 5 and the odds will be 4. Thus 5 is the answer and C as the answer choice.
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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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04 May 2015, 19:39
1
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Expert's post
Hi braveally,

The GMAT cannot realistically expect you to work through 25 digits one at a time, so this question MUST have a pattern to it.

There are certain pieces of information that you're expected to have memorized (formulas, math and grammar rules, etc.) and other types of information that would be beneficial to have memorized (fraction-to-decimal conversions, commonly tested 'patterns', etc.). It shouldn't be difficult to memorize the decimal equivalent of a set of fractions, BUT if you don't want to, then that's fine - the work will just take a little longer.

So the question in this case becomes "how quickly can you mathematically determine that 6/11 = .5454 repeating?" You were concerned that the work would be time-sensitive, so you didn't attempt it. But I'm curious about how quickly you COULD have done it. Grab a timer and find out. I bet it takes 10-15 seconds (at most) until you have the proof that you need.

GMAT assassins aren't born, they're made,
Rich
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3410 [1], given: 172 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 1648 Kudos [?]: 839 [0], given: 2 Location: United States (CA) Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 24 May 2016, 10:45 Bunuel wrote: What is the 25th digit to the right of the decimal point in the decimal form of 6/11? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 To solve this question, we first have to use some long division. This long division allows us to get 6/11 in decimal form, which is 0.545454… where “54” is repeating. We can see that the 1st, 3rd, 5th (and so on) digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th (and so on) digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4. Because we are being asked about the 25th digit to the right of the decimal point and we see that 25 is odd, we know that the 25th digit is a 5. Answer C. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Kudos [?]: 839 [0], given: 2 Manager Joined: 20 Mar 2015 Posts: 64 Kudos [?]: 32 [0], given: 9 Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 23 Jun 2016, 03:42 Aximili85 wrote: C) 5 Same solution as above, but in case the repeating digits are more numerous then see: 1) Number of repeating digits (in this case 2 -> .5454..) 2) Divide the # of the digit you're supposed to view (25th digit) by # of repeats = (25/2)th digit 3) If no remainder, then its 4, if there's a Remainder = 1 then it has to be the next digit or 5, as in this case If remainder is 2 then, 2+1? Kudos [?]: 32 [0], given: 9 BSchool Forum Moderator Joined: 12 Aug 2015 Posts: 2212 Kudos [?]: 836 [2], given: 595 Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 30 Aug 2016, 15:25 2 This post received KUDOS Another way of solving this one=> 6/11=> multiply 9 to both he numerator and denominator => 54/99 hence the decimal expansion would be 0.54545454545454 Clearly the 57th digit is 5=> Smash that C Why did we write 6/11 as 54/99 => if denominator and numerator have same number of digits and if the denominator can be written as 10^n-1 ie 9,99,999,9999 etc then we need not carry any division process . The result would be given by the numerator E.g => 69/99 = 0.69696969... 3/9=0.33333... 158/999=0.158158158... _________________ Give me a hell yeah ...!!!!! Kudos [?]: 836 [2], given: 595 Director Joined: 02 Sep 2016 Posts: 776 Kudos [?]: 41 [0], given: 267 Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 01 Apr 2017, 06:12 6/11=0.545454545454..................... We have to only look at the digit at odd's place because 25 is odd. Therefore the answer is 5. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Kudos [?]: 41 [0], given: 267 Intern Joined: 12 Jan 2017 Posts: 23 Kudos [?]: [0], given: 28 Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 19 Jul 2017, 10:35 EMPOWERgmatRichC wrote: Hi braveally, The GMAT cannot realistically expect you to work through 25 digits one at a time, so this question MUST have a pattern to it. There are certain pieces of information that you're expected to have memorized (formulas, math and grammar rules, etc.) and other types of information that would be beneficial to have memorized (fraction-to-decimal conversions, commonly tested 'patterns', etc.). It shouldn't be difficult to memorize the decimal equivalent of a set of fractions, BUT if you don't want to, then that's fine - the work will just take a little longer. So the question in this case becomes "how quickly can you mathematically determine that 6/11 = .5454 repeating?" You were concerned that the work would be time-sensitive, so you didn't attempt it. But I'm curious about how quickly you COULD have done it. Grab a timer and find out. I bet it takes 10-15 seconds (at most) until you have the proof that you need. GMAT assassins aren't born, they're made, Rich Hi Rich, Are you recommending that 6/11 is useful to memorize directly? Of course we can't memorize everything, but is this a common/repeated fraction that would be useful to know directly? Kudos [?]: [0], given: 28 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9980 Kudos [?]: 3410 [1], given: 172 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: What is the 25th digit to the right of the decimal point in [#permalink] ### Show Tags 19 Jul 2017, 17:50 1 This post received KUDOS Expert's post Hi omegan3, I actually recommend to all of my Clients that they memorize the fractions 1/2, 1/3, 1/4..... 1/11. That's just 10 fractions - and I'll bet that you know at least half of them already. Once you know what 1/11 is, it's not very hard to figure out what 6/11 is. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: What is the 25th digit to the right of the decimal point in [#permalink]

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19 Jul 2017, 18:31
EMPOWERgmatRichC wrote:
Hi omegan3,

I actually recommend to all of my Clients that they memorize the fractions 1/2, 1/3, 1/4..... 1/11. That's just 10 fractions - and I'll bet that you know at least half of them already. Once you know what 1/11 is, it's not very hard to figure out what 6/11 is.

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

Thank you, Rich, for sharing your knowledge.

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Re: What is the 25th digit to the right of the decimal point in   [#permalink] 19 Jul 2017, 18:31
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