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divyajoshi12
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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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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divyajoshi12
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.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/1 ... -the-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... fractions/

You should know 1/3, 1/6, 1/7, 1/9, 1/11
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