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x and n are positive integers, such that 7x = 10n–1. What is the 99th smallest possible value of n?
- a)582
- b)588
- c)594
- d)606
- e)612
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
x and n are positive integers, such that 7x = 10n–1. What is the...
7x = 10n–1....10n = 7x + 1
So 7x has to be of type 9, 99, 999, and so on.
Let us check which is the first multiple of 7 in the series..
We can save time by knowing some multiples of 7..
9=7+2...NO
99=70+29...NO, 70+28 is.
999 = 777+210+12...NO
9999=7777+2121+101=7777+2121+70+31...NO
99999=77777+21210+1019=77777+21210+700+280+39....NO
999999=777777+212121+10101=777777+212121+7000+2800+280+21...YES
That is 6 times 9s...Now 999999=106-1
The next multiple in the series will be twice the number of 9s, so 2*6 times 9s or 10^12
Thus 99th smallest value of n will be 99∗6 = 594
So 7x has to be of type 9, 99, 999, and so on.
Let us check which is the first multiple of 7 in the series..
We can save time by knowing some multiples of 7..
9=7+2...NO
99=70+29...NO, 70+28 is.
999 = 777+210+12...NO
9999=7777+2121+101=7777+2121+70+31...NO
99999=77777+21210+1019=77777+21210+700+280+39....NO
999999=777777+212121+10101=777777+212121+7000+2800+280+21...YES
That is 6 times 9s...Now 999999=106-1
The next multiple in the series will be twice the number of 9s, so 2*6 times 9s or 10^12
Thus 99th smallest value of n will be 99∗6 = 594
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Community Answer
x and n are positive integers, such that 7x = 10n–1. What is the...
To find a relationship between x and n, we can solve the equation 7x = 10n for one variable in terms of the other.
Dividing both sides of the equation by 7 gives us:
x = (10/7)n
So, x is equal to (10/7) times n.
This means that x and n are related by a constant factor of 10/7. In other words, n is a multiple of (7/10) and x can be obtained by multiplying n by (10/7).
Dividing both sides of the equation by 7 gives us:
x = (10/7)n
So, x is equal to (10/7) times n.
This means that x and n are related by a constant factor of 10/7. In other words, n is a multiple of (7/10) and x can be obtained by multiplying n by (10/7).
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