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x and n are positive integers, such that 7x = 10^n – 1
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08 Oct 2020, 18:00
08 Oct 2020, 18:00
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x and n are positive integers, such that 7x = \(10^n – 1\). What is the 99th smallest possible value of n?
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Re: x and n are positive integers, such that 7x = 10^n – 1
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09 Oct 2020, 06:27
09 Oct 2020, 06:27
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lazyashell wrote:
x and n are positive integers, such that \(7x = 10^n – 1\). What is the 99th smallest possible value of n?
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594
I think this question is beyond the scope of the GRE.
First of all, it requires knowledge of the divisibility rule for 7, which I've never seen tested on the GRE.
The idea here is that, if n is a multiple of 6, then \(10^n – 1\) is a multiple of 7.
So, for example, if n = 6, then \(10^n – 1\) is a multiple of 7
Likewise, if n = 12, then \(10^n – 1\) is a multiple of 7.
And, if n = 18, then \(10^n – 1\) is a multiple of 7.
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etc
Since n = 6 the SMALLEST value of n that yields a multiple of 7 in the form \(10^n – 1\), then n = (99)(6) will be the 99th smallest value of n that yields a multiple of 7.
Re: x and n are positive integers, such that 7x = 10^n 1
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10 Aug 2024, 19:20
10 Aug 2024, 19:20
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