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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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100% (01:17) wrong based on 2 sessions
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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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