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09 Sep 2018, 08:53
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
57% (01:33) correct
43%
(01:36)
wrong
based on 429
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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.
A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.
10 Sep 2018, 09:19
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divyajoshi12
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)
23 Aug 2019, 09:11
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philipssonicare
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
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.
