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Bunuel
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What is sum of the eighty-third and eighty-fourth digits to the right 17 Jun 2019, 01:48
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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:

55% (hard)

Question Stats:

71% (02:29) correct 29% (02:36) wrong based on 909 sessions

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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
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B
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CareerGeek
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What is sum of the eighty-third and eighty-fourth digits to the right 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
Show more

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
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Sreeragc
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What is sum of the eighty-third and eighty-fourth digits to the right 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

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
Show more



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??
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CareerGeek
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What is sum of the eighty-third and eighty-fourth digits to the right 21 Jun 2019, 12:10
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Sreeragc
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

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??
Show more

Hi Sreeragc

No my method is not a shortcut, you can directly do it using division method and find out.

My method in this question is useful for someone who is extremely good with numbers or in this case those who would understand by looking at 27 that it can't be converted to a 9 or 99 as both of them are not factors of 27, but 999 is!
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What is sum of the eighty-third and eighty-fourth digits to the right 02 Jul 2023, 02:06
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Sreeragc
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

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??
Show more

Once you know the above concept, you can use it to get more efficient. Finding the factor 37 shouldn't be a problem when you know what to anticipate. You can follow the below method to find the factor so as to get 9 or 99 or 999...in the denominator:-
27x = 9 or 99 or 999 or 9999....
So x = 999/27 ( I am discarding 9 and 99 because you can easily make out they aren't divisible by 27)
reducing the fraction you will get 37 in no time.

The method looks time consuming, but it isn't.
All the best.
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What is sum of the eighty-third and eighty-fourth digits to the right 03 Feb 2026, 02:34
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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
Show more
Some questions are better when done without any trick. 7/9 can be written as 0.777777... Now on diving by 3, we see it reduces to 0.259259... 3 digit repeating. So 84 digit (multiple of 3) will be 9 and thus 83 digit will be 5. Ans = 5+9 = 14

B.
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