(N-1) = (N-2) - 1 is an equation with a unique solution?

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The answer explanation to a GMAT Prep question reads as follows:

"... combining 1/5(N-1) = P - 1 and 1/4(N-2) = P, it follows that (N-1) = (N-2) - 1. This is a linear equation in N and can be solved for a unique value of N."

First of all, when I combine the first two equations, I get 13/10 = (1/20)N, which gives me N = 26. How are they getting the equation (N-1) = (N-2) - 1, and how is that a linear equation with a unique solution? Isolating N, we get 0 = -2, which is false.

It's been a long day, and perhaps I am missing something obvious. But right now I am quite perplexed by this.

Thanks

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by 800_or_bust » Wed Jun 29, 2016 10:46 am
jimmy.steve88 wrote:The answer explanation to a GMAT Prep question reads as follows:

"... combining 1/5(N-1) = P - 1 and 1/4(N-2) = P, it follows that (N-1) = (N-2) - 1. This is a linear equation in N and can be solved for a unique value of N."

First of all, when I combine the first two equations, I get 13/10 = (1/20)N, which gives me N = 26. How are they getting the equation (N-1) = (N-2) - 1, and how is that a linear equation with a unique solution? Isolating N, we get 0 = -2, which is false.

It's been a long day, and perhaps I am missing something obvious. But right now I am quite perplexed by this.

Thanks
You're correct about the first two equations implying that N = 26. It looks they meant to say 1/5(N-1) = 1/4(N-2) - 1, but forgot to include both fractions. Was this from the official GMAT Prep software?
800 or bust!

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by jimmy.steve88 » Wed Jun 29, 2016 2:30 pm
You're correct about the first two equations implying that N = 26. It looks they meant to say 1/5(N-1) = 1/4(N-2) - 1, but forgot to include both fractions. Was this from the official GMAT Prep software?
Yes, this was from the official GMAT Prep software. I think you're right; I'm noticing a number of typographical errors in their software (e.g. 3^3 and 5^3 are written as 33 and 53, etc.). It can be a bit frustrating...

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by Matt@VeritasPrep » Fri Jul 08, 2016 2:37 pm
I think they mean

(n - 1)/5 = p - 1
(n - 2)/4 = p

That would give us the unique solution n = 26, p = 6.