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17 Jun 2019, 01:48
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B
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Difficulty:
45%
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Question Stats:
71% (02:37) correct
29%
(02:34)
wrong
based on 526
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What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction 7/27 is written as a repeating decimal?
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
17 Jun 2019, 02:53
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Bunuel
What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction 7/27 is written as a repeating decimal?
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
Nice Question!
Concept: Make the denominator as either a 9 or 99 or 999
Eg: 2/9 = 0.222222.....
42/99 = 0.42424242.......
547/999 = 0.547547547..........
Given number = 7/27 = (7*37)/(27*37) = 259/999 = 0.259259259....... [We can visualize 9 is recurring at all multiple of 3 digits]
83rd digit = (3*27 + 2)th digit= 5
84th digit = (3*28)th digit = 9
Sum = 5 + 9 = 14
IMO Option B
Pls Hit Kudos if you like the solution
General Discussion
21 Jun 2019, 12:01
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Dillesh4096
Bunuel
What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction 7/27 is written as a repeating decimal?
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
(A) 16
(B) 14
(C) 12
(D) 7
(E) 5
Nice Question!
Concept: Make the denominator as either a 9 or 99 or 999
Eg: 2/9 = 0.222222.....
42/99 = 0.42424242.......
547/999 = 0.547547547..........
Given number = 7/27 = (7*37)/(27*37) = 259/999 = 0.259259259....... [We can visualize 9 is recurring at all multiple of 3 digits]
83rd digit = (3*27 + 2)th digit= 5
84th digit = (3*28)th digit = 9
Sum = 5 + 9 = 14
IMO Option B
Pls Hit Kudos if you like the solution
Why do we need to convert it to a ,9,99,999 denominator fraction where we can directly get the decimals by the division of given fraction. Finding the number 37 may kill a lot more time it seems. Isn't it?
Is this an kind of shortcut??
