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Which of the following fractions when expressed as repeating decimals

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Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 09 Sep 2018, 08:53
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Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.
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Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 10 Sep 2018, 09:19
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divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.


Note:-
1) Prime numbers in the denominator except 2 and 5 yield repeating decimals, no matter what is the numerator.If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
2) 1/3 = 0.3333…, 1/7=0.142857142857.., 1/11=0.090909...
3) Multiplying any integer value with 1/3 or 1/7 or 1/11 or 1/(prime number except 2,5) only shifts the decimal point.
4) As long as the fraction is in lowest terms, the numerator doesn’t matter at all.
Let's simplify options:-
A. 17/44=(17/\(2^2\))*1/11 ; 17/4 has no role here. The number of recurring decimals(with different digits) solely depends on the number of recurring decimals of 1/11, that is 2.
B. 5/6=(5/2)*1/3; In line with the above reasoning, #recurring decimals would be 1.
C. 41/66=(41/2)*1/3*1/11; #recurring decimals would be 2. (since the #recurring decimals of 1/11 is 2)
D. 1/120=(1/(\(2^3*5\)))*1/3; #recurring decimals would be 1. (since the #recurring decimals of 1/3 is 1)
E. I don't want to break my head here.It must contain the maximum number of repeating decimals(with different digits) by method of elimination.

Ans. (E)
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Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 03 Aug 2019, 06:45
PKN wrote:
divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.


Note:-
1) Prime numbers in the denominator except 2 and 5 yield repeating decimals, no matter what is the numerator.If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
2) 1/3 = 0.3333…, 1/7=0.142857142857.., 1/11=0.090909...
3) Multiplying any integer value with 1/3 or 1/7 or 1/11 or 1/(prime number except 2,5) only shifts the decimal point.
4) As long as the fraction is in lowest terms, the numerator doesn’t matter at all.
Let's simplify options:-
A. 17/44=(17/\(2^2\))*1/11 ; 17/4 has no role here. The number of recurring decimals(with different digits) solely depends on the number of recurring decimals of 1/11, that is 2.
B. 5/6=(5/2)*1/3; In line with the above reasoning, #recurring decimals would be 1.
C. 41/66=(41/2)*1/3*1/11; #recurring decimals would be 2. (since the #recurring decimals of 1/11 is 2)
D. 1/120=(1/(\(2^3*5\)))*1/3; #recurring decimals would be 1. (since the #recurring decimals of 1/3 is 1)
E. I don't want to break my head here.It must contain the maximum number of repeating decimals(with different digits) by method of elimination.

Ans. (E)



If we have 2 primes in the denominator ( other than 2 and 5) then the number of repeating decimals depends on which number? Is the larger prime or the prime with more repeating decimals?

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Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 22 Aug 2019, 03:34
divyajoshi12
Do you have the official explanation?

chetan2u, Gladiator59, VeritasKarishma, Bunuel, generis
Are there another methods other than that explained by PKN?

We should memorise division by which numbers? 3, 7, 11, any others?

Please address @Yashbati 's concern as it is a good point
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Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 23 Aug 2019, 04:39
1
divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.


Check out these posts on terminating/nonterminating decimals:
https://www.veritasprep.com/blog/2013/1 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... fractions/

You should know 1/3, 1/6, 1/7, 1/9, 1/11
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Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

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New post 23 Aug 2019, 09:11
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philipssonicare wrote:
We should memorise division by which numbers? 3, 7, 11, any others?

Please address @Yashbati 's concern as it is a good point



The question in the OP isn't a realistic GMAT problem (partly because to confirm the right answer, E, you need long division). So I wouldn't worry about it much, but PKN's method is about as fast as you can get here.

I cannot imagine a GMAT situation where there would be any advantage to knowing the exact decimal equivalent of 1/7 (which is a six-digit repeating pattern). It should be enough to know that it's roughly 0.14. It is occasionally useful to know the exact decimals of 1/9 and 1/11 though (and how to find related decimal expansions, like 3/11 or 1/99).

yashbhati wrote:
If we have 2 primes in the denominator ( other than 2 and 5) then the number of repeating decimals depends on which number? Is the larger prime or the prime with more repeating decimals?


The theory behind this is miles beyond the GMAT, and you'll never need to know about it for the test. But if you do have a fraction 1/(pq), where p and q are different primes not equal to 2 or 5, then if the decimal equivalent of 1/p repeats in a pattern that is D digits long, and the decimal equivalent of 1/q repeats in a pattern that is E digits long, the decimal of 1/(pq) will repeat in a pattern that is LCM(D, E) (the least common multiple of D and E) digits long.

So for example, since 1/11 repeats in a pattern 2 digits long, and 1/111 repeats in a pattern 3 digits long, 1/(11)(111) = 1/1221 would repeat in a pattern 6 digits long, because 6 is the LCM of 2 and 3. Or, as another example, 1/(7)(11) = 1/77 will repeat in a pattern 6 digits long, because 1/7 has a 6-digit pattern, and 1/11 has a 2-digit pattern, and 6 is the LCM of 6 and 2. You can confirm those results with any calculator.

You'll never need that on the GMAT though.
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Re: Which of the following fractions when expressed as repeating decimals   [#permalink] 23 Aug 2019, 09:11
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