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26 Oct 2021, 07:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
24% (02:11) correct
76%
(02:18)
wrong
based on 214
sessions
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List L contains the 98 repeating decimals 0.010101..., 0.020202..., ..., 0.989898.... If each value in list L is expressed as a fraction in lowest terms, what is the sum of the denominators of all 98 fractions?
(A) 5,096
(B) 5,608
(C) 6,770
(D) 6,894
(E) 9,702
(A) 5,096
(B) 5,608
(C) 6,770
(D) 6,894
(E) 9,702
26 Oct 2021, 08:55
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Bunuel
\(0.010101... = \frac{01}{99}\)
\(0.020202... = \frac{02}{99}\)
\(0.030303... = \frac{03}{99}\)
----
----
----
\(0.989898.... = \frac{98}{99}\)
These are 98 terms
But factors of 99 are {1, 3, 9, 11, 33, 99}
i.e. in Lowest form
\(\frac{3}{99 }= \frac{1}{33}\)
\(\frac{9}{99 }= \frac{1}{11}\)
\(\frac{11}{99 }= \frac{1}{9}\)
\(\frac{33}{99 }= \frac{1}{3}\)
i.e. 98-4 = 94 terms would have denominator 99 and 4 other terms would have denominators as {33, 11, 9, 3}
Sum of all 98 denominators = 99*94+(33+11+9+3) = 9362
ANswer: Option E
Bunuel : Please check options. I hope I am not making any mistake
27 Oct 2021, 06:33
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GMATinsight
I just want to extend your approach-
For factor 33, 33/99 and 66/99 will be reduced to least fraction as 1/3 and 2/3, respectively. So, for both of them 3 will be added i.e. 2*3 = 6
For factor 11, 11/99, 22/99, ...88/99 will be reduced to least fraction as 1/9, 2/9, ... 8/9 (here we will ignore 33 and 66 as they are covered in 33), respectively. So, for all remaining 6 values 9 will be added i.e. 6*9 = 54
Similarly, for factor 9 we will get denominator as 11 for 10 values i.e. 10*11 = 110 and for factor 3 we will get denominator as 33 for 20 values (ignoring repetitions) i.e. 20*33 = 660
Final answer will be : 98*60 + 6 +54 +110 + 660 = 6770
Ans. C
Correct me if I have made some mistake.
I just want to extend your approach-
For factor 33, 33/99 and 66/99 will be reduced to least fraction as 1/3 and 2/3, respectively. So, for both of them 3 will be added i.e. 2*3 = 6
For factor 11, 11/99, 22/99, ...88/99 will be reduced to least fraction as 1/9, 2/9, ... 8/9 (here we will ignore 33 and 66 as they are covered in 33), respectively. So, for all remaining 6 values 9 will be added i.e. 6*9 = 54
Similarly, for factor 9 we will get denominator as 11 for 10 values i.e. 10*11 = 110 and for factor 3 we will get denominator as 33 for 20 values (ignoring repetitions) i.e. 20*33 = 660
Final answer will be : 98*60 + 6 +54 +110 + 660 = 6770
Ans. C
Correct me if I have made some mistake.
