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10 Oct 2017, 21:32
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C
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:
68% (02:19) correct
32%
(02:13)
wrong
based on 746
sessions
History
Date
Time
Result
Not Attempted Yet
The sum of the digits of \(10^x−1\) is equal to 3^8. What is the value of x?
A. 18
B. 243
C. 729
D. 2187
E. 6561
A. 18
B. 243
C. 729
D. 2187
E. 6561
20 Oct 2017, 20:36
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Bunuel
\(10^x-1\) will always lead to a number with digits as 9s...
so \(10^x-1 = 99999...x\) times
sum of digits =\(9+9+9+...x\) times = \(x*9\)
so \(x*9=3^8=3^6*9.......x=3^6=729\)
C
General Discussion
10 Oct 2017, 22:20
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lets generalize this sum,
consider x=1,
10^1 - 1= 9 ------9--- 3^2
x=2,
10^2 - 1=99 ----18---2*3^2
x=3,
10^3 - 1=999----27---3*3^2
x=4,
10^4 - 1=9999---36---4*3^2
similarly,
10^x-1= 999...x times= x*9---- x*3^2
It is given that,
x*3^2 = 3^8
hence, x=3^6
x=729
Answer is option C.
Kudos if it helps.
consider x=1,
10^1 - 1= 9 ------9--- 3^2
x=2,
10^2 - 1=99 ----18---2*3^2
x=3,
10^3 - 1=999----27---3*3^2
x=4,
10^4 - 1=9999---36---4*3^2
similarly,
10^x-1= 999...x times= x*9---- x*3^2
It is given that,
x*3^2 = 3^8
hence, x=3^6
x=729
Answer is option C.
Kudos if it helps.
